With iOS 7 and Apple Configurator, can we prevent user to upgrade the iOS using a cable connecting using iTunes and a PC?

I don't think it will allow you to connect to a PC, only to a Mac. this is only for the task of downloading pictures or videos. It serves no other purpose that I'm aware of.

http://support.apple.com/kb/HT5895

There is no mention of this working with PC and since Apple Configurator is Mac only, then when you activate Supervised mode, you are restricted to that particular Mac, except for transferring images and videos.

I hope this helps.

If you want to play around, I'd say try transfering pictures to iTunes on a PC. I have no idea if this would do anything or not.