i wouldnt panic, its not a social website, by logging into office you allow him to connect to his skydrive which will let him send saved items to his skydrive folders.
removing the account by signing out wont do any damage either it just means that if he had another computer ie a work computer at an office the two would no longer sync,
what work you save at the office you can open at home later, as he is at school it wont be a problem.
if he is unlikely to save his work to skydrive then sign out,if he would find it useful (i do ) then leave it signed in.