You may want to be careful regarding the different possible meanings of "can"
a) They have the technical means to do it (sounds more like a bluff than anything else)
b) Your use of the system makes the device subject to the school's rules and regulations, and that includes an obligation for you to give out the mentioned information (possible, you'll have to check the "acceptable use policy" of the school wifi and other applicable laws and regulations like CIPA)
If in doubt - don't use it (the school's wifi, use something else), it shouldn't be that bad...
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