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does fusible webbing hold permantly?

I want to use fusible webbing for a applique on a baby quilt. Will it hold without sewing too? Thank you

It'll hold fairly well, but for a baby quilt, I'd stitch the edges just to be safe. The webbing will peel if it's yanked on (or chewed on) too much, and we wouldn't want to create a choking hazard.
For non-baby applications, you might also look into a product called Badge Magic, which is a peel-and-stick product sold for attaching Boy Scout badges to the uniforms without sewing. I have found that it holds much better than fusible webbing.