Hot glue is basically melted plastic, not water- or solvent-based. Unlike regular glue (which is conductive until the solvent evaporates) It's exactly the same stuff when solid as it is when liquid, so it should be nonconductive whether it's hot or cold. I've tested circuits immediately after applying it, with no problems.
Also, if you don't go too crazy with it, you should be able to pick it off if you mess up, or need to make any changes. (Just enough to cover the end of your wire and adhere it to the board should be enough.) You'll want to remove as much as possible though, around the area you're re-soldering, as any remaining will melt quickly under the heat of a soldering iron, and could make a big mess, not to mention ruining your solder... Once you've got things working again, just re-apply the glue and you're all set.