Not relevant. The school can already seize Suzy's purse and search it on a reasonable suspicion - the cell phone will almost certainly turn out to be no different. They can't simply steal Suzy's purse, but they can hold it and search it. Google up New Jersey v. T.L.O. for the relevant case law.
I should think that virtually any court would rule instantly that ''due process'' consists of rather more than some a&&wipe principal's diktat.
You'd be wrong. In loco parentis goes a long, long way in these cases.
The physical seizure is a huge problem. If seizing a cellphone by simple diktat is allowable, then name me any personal property that can not be similarly seized. Money? Sure, why not -- might be drug profits, after all. Car keys? Sure, why not -- might have drugs or (gasp!) guns stashed somewhere within the vehicle.
New Jersey v. TLO is/was a different kettle of fish entirely, and a poor citation for your argument against a student's property rights. When a person is seen smoking, and smoking is prohibited by rule in a given area, it is completely reasonable to postulate that said person has more cigarettes either on his person or otherwise readily available, as for instance in a purse. In any case, the purse was searched, not seized except during the search; only the then-discovered contraband was seized.
In the case of a cellphone, no such precursor action as illicit smoking exists, and there are therefore no grounds whatever for any seizure of any duration.