Can you downgrade iOS via Backup?

for example. If I have an iPhone with iOS 6.1.X (or any previous version) and I use iTunes to back up my phone to my computers hard drive, then I install iOS 7 (NOT beta, but the actual public release when it comes out), Could I just restore the phone from that backup and as a result it will be downgraded back to whatever version it was when I did the backup? Just like a complete system image on a PC, which will completely restore whatever OS is installed regardless of any changes/updates/etc.

Answers