Cute pattern! Yes, you can applique felted wool to cotton (my avatar uses the cheap plastic felt, but I have done wool on cotton & it works fine).
Typically, applique is done prior to piecing. This isn't quite as important with wool because you bond it to the fabric with fusible web, so there usually is little to no take up in the fabric. Still, with the pillowcase method, it would be difficult to get nice, even blanket stitches as you get closer to the end seam. I would definitely recommend doing the applique first & then stitching your seams.