I was thinking more along the lines of stitching the fleece to the outside edge to retain the waterproof nature of the tarp. Spray adhesive is a good idea. It's more about creating a multi-use 'utility tarp/blanket' than to mock up a bivy.

On the other hand, the waterproof aspect could be satisfied by something like Tyvek, without mission creep. The mylar would need to be slit, and the final sandwich would be Tyvek/Mylar/Fleece. Stitching the fleece to the mylar wouldn't be an issue since the mylar needs perforation anyway. Spray adhesive between the mylar and Tyvek seems like it might clog the vapor permeability of the Tyvek.