Yes, I put batting in the sashing. I generally refer to this as SEMI QAYG, because with the batting as a foundation, it is already firmly attached to the top. The back needs only minimal quilting.
I make at least 3 at a time to ease chain piecing.
I first, I made blocks that just kept getting bigger. they end up looking clunky and being unmanageable. I cut my foundations to a convenient size, make the blocks whenever I feel like it and keep a 'file' of them. When I have enough, I put together a quilt. Actually, I make them both 10.5" and 11.5". The larger ones are for HSTs with a solid fabric on the other half.
I had a bunch of scraps of cotton batting, so I used those for foundation first. Now I am using old sheets. I used up mine then picked up some at a thrift store. (and washed them with bleach to be on the safe side). Small holes don't even matter. The sheets are easier to handle but dont have the body of the batting version.