I agree with Rubick that sanctioning the rhyming of many with plenty and twenty is a gross injustice to the language. However, in instances of "off-rhyme", even the classic poets have be known to stretch it a bit in a pinch.
That being said, I propose, by venturing into sound linguitics, that even in the so-called "silent T" pronunication of those words that it is rather a "soft T" coming off the N. If you do a crisp T you'll see that the tongue clicks off the forward roof of your mouth toward or even on the upper teeth. But coming off the N in a "nt" pronunciation, the tongue instead jumps further back onto the roof of the mouth producing more of a roll than a click. I habitually use the "soft T" pronunciation for twenty and plenty and other "nt" words, but mentally I'm aware of pronouncing the T and still see it, and consider it present in those words. So, no, I would never consider sanctioning that as a valid rhyme.