I agree with Janet. Just make sure to window your fusible so it's not so stiff.
Also wanted to mention that most of the quilts I've ever seen win major shows were not done needle turn. They were, however, done with a turned edge. There are plenty of different methods out there for that from freezer paper to AppliQuick to Applipiecing and so forth, plus the ones where you use water soluble stabilizer on the back to create a pillowcase edge. All of those can be done by machine.
If you really want to stick with the true raw edge design using the straight stitch in a juried show, I would suggest maybe brushing or otherwise distressing the edges so it's clear that it was done for artistic purposes to create that frayed/fuzzy look. Having a raw edge with just one or two stray threads here or there might not read as a design choice in a juried show. That said, if it's not a juried show -- go for it! There are many wonderful quilts out there done with that basic stitch and they carry their own beauty that is beloved and respected by many quilters and quilt-lovers.