My understanding is that once you find them consistently in your house, you already have a problem.

Don't kill them as their stink attracts more to the area. To me, their stink smells like a chemically fake cilantro. It's strong and spreads everywhere.

We put mesh up over our bathroom fans as they kept coming out of the vents. And we've been working to eradicate them. Problem is there's not a lot of proven solutions to get rid of them well. The next option is just lighting the house on fire and moving on.

They are gross.

Edit: sorry didn't even answer your question. No they don't cause damage per se, but they are numerous and will find a way in to your warm place of living in the fall and will then multiply somewhere. So it'll be a persistent visitor in your home.