No.
Your computer can, of course, catch a virus if you download an executable program from an untrustworthy site and then, of your own free will, double-click on it in your file manager (or Mac desktop, or...). This is the same risk you run when downloading programs from bulletin board systems or via anonymous FTP.
Viewing images, filling out forms and so on is harmless. So, most likely, is downloading a program from a respectable source with a reputation to protect.
