That's an interesting question. And it is one that doesn't come up frequently. The short answer is yes, it is possible for printers to be infected/hacked/remote controlled. The longer answer is that it is harder to do it to a printer than a PC. So infections are rare and mostly involve network printers. And as for scanning for viruses on a printer, none of the AVs actually scan them as far as I know, so leaving them connected would not make any difference. One way to make sure is to only connect the printer when you need it. Otherwise, leave it off. That's what I do.
Here's an interesting article on the subject. (It's from last year, but still worth a read)The Surprising Security Threat: Your Printers