While most people do not think about Paul as a mystic, his conversion experience can be seen as a mystical experience. Albert Schweitzer considered Paul to be a mystic, writing a whole book on the subject. But apart from whether Paul was a mystic, there is still the question of the influence of Pauline thought on the history of mysticism.
Schweitzer distinguished between primitive and developed mysticism. The first is mysticism that has not risen to the level of a conception of the universal. It still involves views about the earthly and super earthly, temporal and eternal. The second is what he calls "intellectual" mysticism. It distinguishes between appearance and reality. It sees the eternal in the temporal. Plato would fit here, as would Stoicism, Spinoza, Eckhart, and Hegel.
For Schweitzer, Paul is somewhere between these two types. The religious conceptions are more advanced than primitive mysticism, yet there is still differentiation. Humans do not become one with God, yet God is seen through everything. Schweitzer puts it,
"In Paul there is no God mysticism; only a Christ mysticism. . .The fundamental thought of Pauline mysticism runs thus: I am in Christ; in Him I know myself as a being who is raised above this sensuous, sinful, and transient world and already belongs to the transcendent; in Him I am assured of resurrection; in Him I am a child of God."
This includes the idea that being in Christ is conceived as having died and risen with Him, and the consequence of this is that the participant is freed from all sin and from the law, and assured of resurrection.
Note that this conception of mysticism is significantly different from that of Plato, if indeed there is mysticism here at all.
1. For one thing, the steady intellectual ascent that Plato advocates is absent from Paul. In fact, it's not really even a moral ascent. It is more a volitional ascent, a decision of the will to surrender more & more to Christ. Conversion is a first step on this path, but if that was all there was to it, Paul would never have written to Christians about the importance of letting Christ live through you.
This distinction is an important one in mysticism. Many mystics tie them together, but their roots are quite different. When a writer talks about the ascent of the soul, we might ask what exactly is involved in that ascent, and what is actually ascending.
At any rate, if Paul has a mysticism at all, it is in union with Christ. We do not become God; rather, Christ lives through us. For Paul, this results in intellectual and moral change. One goes from the "old man" to the "new man".
2. Plato's necessarily takes us out of the material world; Paul's does not. In fact, in Paul's eschatology, it is the redemption of the physical world that is at issue, not its destruction. Christ came back onto a material body. At the end, humans will be physically brought back (resurrected), not just spiritually brought back or reborn into a different body. This is important, because it means that there is a strain of mysticism that is not world denying.
3. Paul's mysticism is almost completely devoid of symbol and metaphor. The followers of Plato use symbol extensively, to the point that it is solidified into reality. For instance, the symbol of death, part of many kinds of mysticism, is a single transition from purgation to illumination. For Paul, it is an experience which constantly recurs. We die every day to self. We are constantly renewed.
4. Schweitzer argues for a fourth difference, although this is more a difference between Paul and Hellenistic religion rather than Plato. Paul's mysticism is, as he puts it, "historico cosmic", while that of Hellenistic religions is "mythical". The first looks forward, the second looks back. Looking back involves using a symbol to re experience an event of the past. The symbol acquires universal significance, and its repetition brings the myth to the present. In the second, the whole movement is toward a fulfillment.
5. The mysticism of Plato is individualistic (and indeed, this is the overwhelming trend in the history of mysticism). The mysticism of Paul, on the other hand, is collectivistic. It drives the person toward community, rather than out of society. Furthermore, the mysticism of Paul is not esoteric, as is so often the case, but is exoteric. This may well have been a heritage of his Jewish roots.
Apart from the theology, there are two instances in Paul's life that speak of a mystical experience. The first is the report of his conversion, in Acts 9:1-19. The second is an account, told about someone else but usually attributed to Paul, in II Corinthians 12: 1-13. The first is a visionary account. Some would not consider it mystical proper, because it is not ineffable. The second, however, would be mystical. It is interesting that there is a hint of this given, and yet Paul feels constrained to only hint at it, and talk about the physical ailment he has to keep him from getting proud.
Acts 9: 1-19
1 Then Saul, still breathing threats and murder against the disciples of the Lord, went to the high priest 2and asked letters from him to the synagogues of Damascus, so that if he found any who were of the Way, whether men or women, he might bring them bound to Jerusalem.
II Corinthians 12: 1-13
1 It is doubtless[a] not profitable for me to boast. I will come to visions and revelations of the Lord: 2I know a man in Christ who fourteen years ago--whether in the body I do not know, or whether out of the body I do not know, God knows--such a one was caught up to the third heaven. 3And I know such a man--whether in the body or out of the body I do not know, God knows-- 4how he was caught up into Paradise and heard inexpressible words, which it is not lawful for a man to utter. 5Of such a one I will boast; yet of myself I will not boast, except in my infirmities. 6For though I might desire to boast, I will not be a fool; for I will speak the truth. But I refrain, lest anyone should think of me above what he sees me to be or hears from me.
The Thorn in the Flesh
7And lest I should be exalted above measure by the abundance of the revelations, a thorn in the flesh was given to me, a messenger of Satan to buffet me, lest I be exalted above measure. 8Concerning this thing I pleaded with the Lord three times that it might depart from me. 9And He said to me, "My grace is sufficient for you, for My strength is made perfect in weakness." Therefore most gladly I will rather boast in my infirmities, that the power of Christ may rest upon me. 10Therefore I take pleasure in infirmities, in reproaches, in needs, in persecutions, in distresses, for Christ's sake. For when I am weak, then I am strong.
Signs of an Apostle
11I have become a fool in boasting;[b] you have compelled me. For I ought to have been commended by you; for in nothing was I behind the most eminent apostles, though I am nothing. 12Truly the signs of an apostle were accomplished among you with all perseverance, in signs and wonders and mighty deeds. 13For what is it in which you were inferior to other churches, except that I myself was not burdensome to you? Forgive me this wrong!
At any rate, while Greek thinkers are important in the history of mysticism, Christian thought is even more so. Greek thinkers provide much of the framework in which mysticism can occur; Christian thinkers provide the content. What is the form of the Good for Plato becomes God for the Christians.
But the ambiguities of Christian doctrine make mysticism a problemmatic enterprise. Some regard it as extra revelation (even though in most true mysticism there is no content at all), and reject mysticism as pagan or even demonic. The Platonic movement to union with the one has been interpreted as the human becoming God. The mystical experience is not one that can be legislated by the church, and so mystics can seem like "Lone Rangers", out of control. So, mysticism has often had a cool or even hostile reception in Christian circles. It is part of the reason why it has never been part of the canon of church doctrine, and is rarely studied in seminary.