I have a beautiful lap quilt that my DMIL made. She gave it to me for Christmas 11 years ago. The label has a raw edged rose applique on it. Because the kids were not careful with it, I had to wash it several times. The fabric has faded, the binding is frayed, but the applique is not frayed. I just looked at it. She did a tiny zig zag stitch that was right on the edge. It's held up for 11 years and several washings.
Why not do a test. Get a square of fabric and hem or serge the edges. Do a raw edge applique on it and then throw it into your laundry and have it go through several loads and see how it holds up.
Remember raw edge applique is not the same as frayed edge applique.
I have done applique the way Eleanor Burns does it. It works great on flowers and such, but if you have tiny or intricate pieces it won't work.