Mods, can we get this moved to the Older Editions forum, or the subject fixed to mark that it's for 1E AD&D? Some folks seem to be missing that, and it's causing confusion.
As for the original question, certainly they can hold off, but IMO the DM should just be able to upscale the difficulty on the modules a bit. Add a few HP to the monsters, etc. It's really not a big deal to be one level over the recommended.
@JMISBEST , as you've already noted, these characters seem to already be a bit more powerful than average with their high ability scores and multiple monster companions, so the DM would theoretically be tweaking a little already.