OFFHAND, I don't know why it would NOT work. One thing I'd wonder about is if the M1A rifling twist, which is optimized for 147 - 175 gr. projectiles, will stabilize the lighter projectiles. I'm also guessing you'd have to push them pretty fast, if you hope to operate the action. I did a quick search over at the Hodgdon reloading site, and most of the data I found, using service-rifle friendly powders, involved compressed charges. The exception, H335, might be the powder to work with.
I don't know what rifle powders you might have on hand, but if they're near the 4895s, you might try a work-up with those.