No, they do not. The Supreme Court ruled incorrectly in Morse v. Frederick. Oppressive governments and other institutions infringe on people's free speech rights frequently. The fact that their administrative organs reaffirm those infringements on appeal does not annul the infringements; it merely adds insult to injury.
I wasn't really speaking as to the morality of the thing, more so just arguing the reality of today's legal situations in the US. According to current US Supreme Court precedent, its an acceptable abridgement to a student's speech within the bounds of constitutionality. Not saying that its right or wrong, only sharing what a court would usually find today if you made that argument.