You can turn under the applique edge if you want. It's faster to fuse, but it's not a requirement when using blanket stitch. Old-fashioned applique was often done with turned-under edges and hand blanket stitch; you can simply substitute a machine blanket stitch for the hand stitching.
If using a machine blanket stitch, it helps to use a heavier than normal thread or to treat two regular threads as one, using two spools and then running the threads together through the tensions and needle. Makes the blanket stitch more visible.
I don't know about working with felt unless it is felted wool. The edges of felted wool don't ravel, which is why you don't turn under those edges when doing blanket stitch -- whether by hand or machine.