What does an inducer do on a hvac system. Is it a problem if the gasket is bad on the inducer?

I assume you are talking about a furnace / boiler inducer.. it is the blower / fan that pulls or pushes the combustion air or gases through the unit to exhaust the products of combustion to the exhaust / vent system and to the outdoors. A bad gasket can be a BAD thing depending on where it is located. If on the exhaust side of the blower, gases will escape there rather than go out the vent piping. If on the intake side of the blower, it will pull air in there easier than through the unit, and cause a safety air pressure switch to open and shut down the unit, depending on how bad the gasket leak. This issue is best checked by a qualified heating / AC contractor and repaired!

A powered blower enables the furnace to use smaller vent pipes. They are even more important if the combustion air is ducted in from the outside.

Yes a leaky gasket can be a serious problem. Since you were competent enough find the problem, you may be able to fix it too. Just check your work carefully.