Within Christian mysticism, I've not really heard the term 'mysticism' or 'mystic' applied to any Pentecostal Christian. And yet, it seems, their spirituality is such that the name mystic, or mystical would be an apt description.
The hallmark 'speaking in other tongues' is very mystical in its application. The purpose of speaking in other tongues is to bypass the dianoia-mind (rational mind), and access the spirit directly. Also, when one is 'in the Spirit' as Scripture states, one is at that time open to all the gifts of the Holy Spirit, which Scripture lists 9 (1Cor 12). Not only so, but it was while the apostle John was in the Spirit, that He received his apocalyptic visions recorded in the book of Revelation.
I can say from an experiential standpoint that there are heights in the Spirit to which I would not have ascended had I not been baptized in the Holy Spirit, as a Christian, as evidenced by speaking in other tongues. I'm not saying that other mystical experiences could not be known by other Christian denominations which do not adhere to Pentecost, be they Catholic, or Protestant. But I am saying that there just are certain places in the heavenlies one cannot traverse without this experience. These places directly involve speaking, praying, or singing in tongues as Scriptures teach. This is obvious as some schools of thought exclude either the gifts, tongues phenomenon, or strictly limit tongues to some select few who receive this gift. (one may at this point reference my other blog, "In House" under the topic "Confusing the Gift with His Gifts" for clarification on this point in the Christian debate).
Yet I think, and implement in my own practice praying in tongues as part of my mysticism, to which was referred to in part in an earlier blog (pertaining to the neshamot). As part of what would be called dhikr in Sufism, or joppa, in Hindu and Buddhist mysticism, speaking in tongues helps to polish the heart in hopes of seeing God as Jesus spoke of (Mt 5). This also helps to refocus the mind when it strays as it invariably will during the first stages of practice, or in the practitioner who is yet undisciplined on the mystic path.
If you are Pentecostal Christian, and consider this as part of a mystical practice, just keep in mind that whether there be tongues they shall cease when that which is perfect is come (1Cor 13). Which means in our Quest that when the tongues have done their part in setting our self aside, and polishing our heart, there will come a time of silence. For us, this is soon after neshamah-behemot, and heshamah-nepheshi have been opened up, as subtlties, and we are now in a place of silence before Him, awaiting visions from Him.
Thank God for a means of setting aside the ego, and stilling the mind, and polishing the mirror of the heart through prayer and worship in tongues, as we may now await the divine Image.