I've got a corrupt neighborhood that is very old, with a LARGE number of sims living in there for many generations. I had all kinds of crazy things happen with sims becoming glitchy to the point of being uncontrollable, sims changing into the wrong age group or losing their face when aging, etc.

I was wondering, if I package a bunch of sims onto one lot (using a cheat code to allow many to move in and preserve their relationships), and then move that lot to a new neighborhood, could that new neighborhood become corrupted as well, because the sims on the imported lot are corrupt? Or does it not work that way?

Yes, that would corrupt your new neighbourhood - not just because the sims are corrupt; moving any sims, including totally problem-free sims, between neighbourhoods will corrupt both neighbourhoods.

The best way, if you want to save your sims, is to extract their appearances and recreate them: Game Help:Moving Sims^wiki