Yes you can machine quilt a wool quilt. You need to consider the nature of the fabric you are using.
Thin batting
If I put wool fabric on the back I would make sure it is a thin light weight wool fabric.
Lengthen your stitch to accommodate the extra thickness of the fabric.
I would be sure and use cotton thread.
Walking foot definitely.
Longer stitches if free motion quilting.
Baste well and then do extra pinning in front of pressure feet to help hold layers together.
Practice on a piece first to get the feel of it.
Lots of support to hold the quilt from pulling away from the machine.
Take a class in weight lifting before you start in order to hold up all that weight.....lol