Of course not.
But thou when thou shalt pray, enter into thy chamber, and having shut the door, pray to thy Father in secret: and thy Father who seeth in secret will repay thee.(Matt 6:6)
I'm pretty sure there that hesychasm is not summarized in that verse. Where is the use of stillness/quiet/silence/hesychia?
Even if it was there, that is not a proof text that qualifies all of the meditation techniques involved as being distinctly apostolic in origin. Do the Orientals practice hesychasm? Nope. Do the Latins? Nope. Do the Nestorians? Nope. Any Protestants? Nope. Well, it looks like it's just the Byzantines on this one, kids. If the practice had existed since early apostolic times, then it would be in more than one geographically isolated communion. Hell, do the Arab Orthodox in the Greek tradition practice it? I don't even think I've come across anything showing that they do. Maybe they do, but that wouldn't change anything.
You are getting so huffy and snarly about "post-schism innovations", and it's a real bore. Hesychasm as the specific discipline that currently exists developed
in the East after the schism. Sure, there are plenty of precursors to it in Eastern patristics leading up to the schism, but there was no uniform practice that was Catholic in nature. The Latins had their own Western Fathers who's ideas gradually developed
into purgatory, the natural extrapolation of their isolated trajectory. I consider hesychasm to be the Eastern equivalent to doctrinal developments like purgatory, the immaculate conception and Papal infallibility.
The term 'innovations' takes on an accusatory tone. "Oh, those Catholics, changing the faith with their innovations
. Well, not us! We haven't had any theological developments since the schism! There's nothing innovative about hesychasm! True-Church-Bot; ascend!"
Perhaps a fair distinction to make is that hesychasm is not dogmatic as far as I know. The energies/essence distinction is, but as far as the whole 'hesychast way', I don't think anyone is actually dogmatically required to pray in that way. Some of the developments in the West are theological in nature, and dogmatic to boot.
But it seems like on both sides both parties are making the same case: That the belief that was clarified post-schism had always existed pre-schism; purgatory or hesychasm. And in a way, both are right in their respective theological spheres. Prototypical thoughts seemed to have been floating around, the ideas were just later synthesized and codified. They had always been to some degree a part of the faith, they were just never sufficiently outlined in cooperation before the split.