If you did a very good job of gluing your good to go. If your unsure pry a small section of tire off the rim. If is tough to do I leave it. If minimal pressure pops the tire loose I’d reglue. With the clear glue Id leave everything in place and add a layer to the rim, let it set a bit then mount the tire. A layeron the tire would probably be prudent, but it would likely depend on how rushed I was.
Removing old glue is such a chore, I’ve never actually done it.
Over time (probably not over winter, but years…) the glue will dry and become brittle. It still holds just fine, but if you were in a training/racing situation and tried to rip off the old tire and put on a spare…it wouldn’t stick well enough to be safe because the old glue on the rim isn’t tacky anymore.