Burbs is right, if you smear a layer of super glue over the right side of the tire, it stiffens the side wall and does not let it roll like it normally would. It makes the tire feel a little harder than it really is.
If the glue on the tire has worn out and the tire is pulling away from the wheel, I will superglue the tire back to the wheel. This isn't the same gluing the side wall. In spec foam tire classes, I've seen drivers super glue the side wall to give them a stiffer tire. This in affect makes a dual compound tire, similar to a plaid in touring. The reason this is necessary is because of high bite track or lack of tire choice. It also can help on a Legends car, since there is limited tuning on the front suspension. The downside to doing this that the glue will need to be reapplied as it wears out or is dissolved by traction compound.
It has been my experience that Paragon will slowly dissolve superglue if it is in direct contact with it.
I've done a lot of superglueing to both the rims and sidewalls. The best superglue to use on the sidewalls is flexable superglue, like Zap Flex-Zap II. This is much better than standard superglue. It strengthens the outer sidewall, yet remains soft and pliable. I apply it with my finger, working a small amount into the foam sidewalls by pressing down a little as I work it around. This glue is slower than traditional CA, so you can get away with doing that technique.
Have any of you used an old slot car trick, that being use a coat or 2 of clear nail polish. this you would have to give some dry time but I wonder if it would work as well,plus doing it at home would give you time to really think about how far you want to go with this method. Meaning 1/2 way up the sidewall or roll it over the top edge.
If you want to glue your sidewall for chunking reasons, but don't want the effect of it stiffening... Try Hobbico canopy glue. It doesn't get eaten by paragon, and is very flexible... just as flexible as the tire.