What is the purpose of the plastic lower engine cover on a Honda Fit?

The lower plastic covers are for aerodynamics. They aren't really needed for function, so aren't a safety item. You should be able to drive them just fine without them.

That said, if you are hearing creaking, it wouldn't be because you are missing these covers. There is something else going on which might make your car unsafe to drive. I'd have it professionally looked at, for peace of mind, if nothing else.