Unfortunately, you cannot. I learned this the hard way when a student came in with a broken device just a few days into the school year. I took a replacement device out to set it up (we Supervise them in Configurator and manage via an MDM) and was forced to update it to iOS 7.
The problem got worse. When I backed up the student's Supervised device (which was running 6.1.3) and restored it onto the newly updated iOS 7 iPad, there was no Supervision profile installed on the device with the backup. Last year, with iOS 6, the Supervision profile was part of the backup and reinstalled on the device when restored from iCloud. This is no longer the case.
So now I had two ipads: one supervised with all data but a broken screen, and a brand new one with iOS 7, all the student data but unsupervised. Not good. I figured at that point I had nothing to lose, so I updated the broken screen device to iOS 7 and all profiles stayed intact. I thought perhaps it was a problem with an older backup on a new OS so I wiped the replacement and put it back to factory and during setup I pulled the iOS 7 Supervised backup onto the new iOS 7 device and again, no Supervision profile. This is an issue since you cannot Supervise after the fact. I have read that Apple was coming out with a way to Supervise OTA but the feature is unavailable as of yet.
Other issues we have experienced: If you are Supervising iPads with Configurator, when you do decide to update to iOS 7, you cannot give students the freedom to update themselves because an OTA update removes the Supervision profile from the device. If you do it manually on your Configurator station, the profile remains intact. For smaller deployments, this is an option; for others, not so much.
All in all, this entire rollout has been a nightmare for schools. There is plenty of chatter around about all of these issues. I thought we would be able to Prepare and Supervise devices without updating to 7 but it appears that is not the case.
Regarding attempts to downgrade to 6.1.3... as of a week or so ago (unfortunately) Apple has stopped signing all versions of iOS 6 for iPad. So even with a complete wipe of an iOS 7 iPad (that was previously iOS 6) in an attempt to restore an old iOS 6 encrypted backup, a restore via iTunes will force the device to check in with Apple and the latest version of iOS 7 will install on the iPad. I've also tried importing an old ipsw file for 6.1.3 into iTunes and into Apple Configurator to try and force loading iOS 6.1.3, but niether iTunes or Apple Configurator will install it.
Found this on another thread.
I followed this support article to use a Custom iOS version and downloaded the ipsw files from the site listed. This has allowed me to supervise devices still without them updating to iOS 7. I'm not sure if this would cause any problems in the future or not.