Do the celebrities actually sign things on eBay?

Well eBay is a website... You can't sign a website.

But to answer your question: There are some people who try to sneak it by and make a signed item, like a Baseball or such. So you have to be very careful on what you buy. Same for all items on eBay. But for stuff like that, usually eBay will refund you and take care of the seller.