Did the Word γυμνάσιον Have a Secret Meaning in the Alexandrian Church?

I have been wondering about this ever since I became interested in the Mar Saba letter.  Could the Hellenized Jews who read about Jacob and God wrestling together at Peniel have imagined that this could have occurred with both men clothed?  Does God even have clothes?  Do angels have a closet of leisure suits?  I don't think so.  One could argue of course that the Hebrews envisioned at Jacob to have been fully dressed, but could the Greek speaking Jews of Alexandrians have imagined a wrestling match taking place with anyone clothed?  I don't know for sure but I don't think so.  Indeed let's remember that Clement explicitly states that Jacob was castrated in the match.  Hard to imagine some supernatural foe doing that while Jacob was dressed for a dinner party.

So given the fact that Clement must have imagined this wrestling bout to have taken place naked doesn't it seem reasonable to suppose that all subsequent allusions to the gymnasion (γυμνάσιον) of virtue would necessarily take us back to two men standing naked before one another.  I don't even think that any physical contact would have to be implied but once again we are back at the idea of the naked disciple standing before a naked Jesus.

We should also note that it would be impossible for any Greek speaker not to be aware that γυμνάσιον derives from the word for 'naked' by means of γυμνάζω (to train naked). So when you start looking at the references to γυμνάσιον in the Alexandrian writers it is strange that we should see ideas of the sacraments of the mysteries of the Church thrown in where we would expect to see Peniel allusions. I happened to be reading Origen's Contra Celsum just now so:

We maintain, indeed, that "human" wisdom is a naked exercise (γυμνάσιον) for the soul, but that "divine" wisdom is the "end" (τέλος) being also termed the "strong" meat of the soul by him who has said that "strong meat belongeth to them that are perfect, even those who by reason of use have their senses exercised (γεγυμνασμένα) to discern both good and evil." [Contra Celsum 14]

But if it should fail any one, it must be through his own fault, in being slothful to partake of this "living bread" and "genuine drink," by means of which the wings, nourished and watered, are fitted for their purpose, even according to the saying of Solomon, the wisest of men, concerning the truly rich man, that "he made to himself wings like an eagle, and returns to the house of his patron." For it became God, who knows how to turn to proper account even those who in their wickedness have apostatized from Him, to place wickedness of this sort in some part of the universe, and to appoint a γυμνάσιον of virtue, wherein those must exercise themselves who would desire to recover in a "lawful manner " the possession (which they had lost); in order that being tested, like gold in the fire, by the wickedness of these, and having exerted themselves to the utmost to prevent anything base injuring their rational nature, they may appear deserving of an ascent to divine things, and may be elevated by the Word to the blessedness which is above all things, and so to speak, to the very summit of goodness [Contra Celsum 44]

There is an unmistakable Platonic sensibility running through this last reference. One wonders if there is something more to the notion of the γυμνάσιον of virtue.