I'm not an expert. All I have to offer is that back in the late 80s I went to a lecture by Phulgenda Sinah, author of . His book claimed that the Bahag Gita was altered by invaders to make Indians more submissive and he claimed to have restored the original through researched interpolation.
Anyway, he made his living teaching yoga, in addition to doing research.
During the lecture he told the audience that hatha yoga goes back further than most people think......even before Hinduism. Ancient coins were found with many of the postures ( asanas ) pictured on them.
The legend is that the historical Buddha, tried all of the various spiritual disciplines he could.
So, the answer is, it is possible, but I don't know
Like many things, I think hatha yoga would be an excellent innovation for monks, but isn't likely to happen beyond isolated individuals due to the iron grip of orthodoxy and tradition.