Of course you can!! Plenty of modifications have been made over the centuries by quilter's. I have no idea what they used before they made batting, but almost all of my personal blankets that we use have those thin fuzzy blankets, similar to the heating ones as the batting. Makes the quilts much warmer than regular batting will.
Couple pieces of advice. 1. DO NOT MACHINE QUILT THIS unless you have a darning foot or a walking foot as it will be VERY thick. 2. Tack if you can to make it easier. Hand quilting with the blanket in the center can be done, it's just more difficult.