I'm sure it can, but I've never used phpmyadmin before so I don't know how you would do it. An option to upload an sql file or run an sql file from the local files system would be things (options, commands?) to look for. I doubt you'll be able to just copy and paste the sql into a form though. I'm willing to bet that the sql backup file is just too big to be uploaded by normal HTTP GET or POST.
-Vinny