While taking the float bowl off the carb a sliver of the housing (edge, lip) cracked off. If we reassemble the carb with the new gasket and some sealer will this affect the running of the carb once we put it back on the bike?

Depends how much cracked off. If there's any gap whatsoever, the gasket will not seal. You don't wanna use sealer on a carb. That stuff can get in the little ports or in the jets and just clog everything up. Unfortunately, if too much cracked off, you may need to get a new or used carb.

To answer the question, no, it will not affect the running, providing that none of the sealer goes astray into the fuel.
If by some horrible chance that the missing pc leave an open void to the outside, I think I would assemble the bowl to the carb first, then push some automotive silicone gasket sealer in to the void, but only enough to fill the void,....no more ! Then let it set up for a day.
What else mite work even better, is reattach the sliver to the bowl w/ JB or equivelent. Seems like a perfect spot for JB because it has no stress on it, and I believe JB is gasoline resistent.