You may then also need to upgrade security, possibly something that needs thinking about first. For instance you may need to consider trying to prevent users not only using a new profile, but prevent access to alternative browsers and the ability to install new browsers.

Next you may need to consider can a user actually bypass your whole OS with removable media.

I am guessing you may be trying to control what younger users may do on your computer, that can become rather difficult because they may well understand them better than we do ourselves.

To answer your question directly, NO it can't be disabled. Mozilla didn't provide a "switch" for that feature to be disabled. That feature doesn't even respect the Parental Controls that are built into Vista and Win7.
There was a bug filed about this issue with the Windows Parental Control issue on 12-31-2008, no work toward fixing this bug, and it hasn't even received a comment from a developer in over a year.
https://bugzilla.mozilla.org/show_bug.cgi?id=471658

see http://kb.mozillazine.org/User:Dickvl/Private_Browsing_disable to disable the Private Browsing menu entry and the Clear Recent History menu

You may also be interested in locking Google into Safe search
"You can tell at a glance if the lock is engaged ... -- even from across the room. "