Folks use felted wool for applique, because it doesn't fray. I love wool batting, but that is light and fluffy.
If you make an entire quilt of felted sweaters, it's going to be very, very, very heavy.
Having said that, there's no reason why you can't try. I would butt the pieces together & zigzag them, or use the QAYG technique that uses 1" sashing strips, which also butts the pieces together but conceals the edges. You could use a cotton fabric for backing, but I would skip the batting.
A small item like a throw or tree skirt would be a good size.