Yuppers. First Amendment means that, as a government agency, you cannot monitor/filter/block/etc what students _say_ in outgoing email. (It's even a seriously sticky situation in government agencies with their employees.)
On the other hand, you _can_ ban individuals from using the equipment _at_all_, if you have a rational reason for doing so. Like they've been using it abusively.
Silly as it seems on the face of it, restricting them from 'saying anything' it not the First Amendment problem that restricting them from 'saying *specific* things' is.
BTW, this is _nothing_ new. 50-70 years ago -- _couldn't_ restrict the *politician's* sound trucks going around trying to drum up votes, at election time. *COULD* ban *all* sound trucks, _all_ the time..
Similarly, a government operation can restrict "what functions" the multiple-purpose box known as an 'Internet-connected computer' is used for, without running afoul of First Amendment.
The critical difference, from a legal viewpoint, is that when you merely restrict the 'use' of the government's equipment, people are free to go use _other_ equipment for the same purpose, and not be encumbered by those restrictions.
[TELECOM Digest Editor's Note: Same thing in Chicago at the Daley Plaza downtown. City said if you want to use loudspeakers or musical instruments we will allow only one set of same each day, generally first come, first served. Otherwise the Democrats on one side of the plaza with their loudspeakers will be drowning out the Republicans on the other side of the plaze with their sound equipment, and the resulting cacophony will keep the public servants working in their offices upstairs distracted. Now you had a legitimate government concern. 'Administrative Convenience' nearly always trumps the First Amendment. PAT]