Can a bad gauge cluster cause other problems?

Yes, if you have a bad cluster, it can cause all kinds of strange problems. Can I ask what problem you are having so I can troubleshoot the problem for you?

I had thought about replacing it because the odometer and tripmeter do not work, probably gears could be replaced...
I'd wondered if maybe it could cause problems with my windows, they are done.
The oil gauge seems "sometimes", sometimes it does, sometimes it doesn't. I don't know if I can rely on the alternator gauge though it does not differ by great amounts.
I do not know what all problems an instrument panel could cause electrically, not much of an idea.
The car does start, it runs; sometimes more smoothly than others, it could be just the age and nature of the car...
The check engine light stays on, though there are many causes for that, but the car runs, runs well enough, so I don't trouble myself.

The windows and check engine light will be separate issues, please start new questions for those problems, but the other problems seem like the cluster need to be replaced, here is how the job is done. You can get a used unit from eBay or search Google. Check out the images (below). Please let us know what happens.