YES! YES!
I finally found video confirmation that this is indeed possible! https://youtu.be/ZJtRbBmPnsM
This is #StreetFighterXMegaMan, specifically the first Shadaloo stage. It IS possible to defeat Balrog before reaching the point where he falls into a pit.
I remember doing this ONCE myself but despite many subsequent attempts I failed to reproduce it. I didn't do it without taking damage, but I did empty his health bar. And I was starting to doubt my own memory. But, no, this is possible, and this video proves it -- while taking no damage, even.