there will always be something for the shrimp to clean up...whether its left over food or poop. shrimp arent picky. you could also drop a piece of an algae wafer in. i doubt the betta would touch that.
i wouldn't really worry i have a Caridina Japonica ( Amano ) shrimp in my community tank i dont put anything in the tank other than fish flakes and he seems to be doing fine.
Shrimps eat all kinds of stuff from what i have noticed from mine. I was told it is an algy eating shrimp but i've seen it stuff his face with frozen blodd worm? go figure that one out
If u find an skeleton ( his skin ) lying about and he's still in there, he's growing therefore u know he's eating