But it may change where the student is registered to vote (e.g., a student from Ohio going to a school in NY may have intended to file an absente ballot in his/her home state, but is now a NY voter).
Republicans wouldn't be registering Democrats to vote in the hope that one of these newly registered won't be able to vote somewhere else where they are already registered.
The intention was to register dope smokers who would likely vote for Democrats but who would otherwise not be motivated to register to vote.
If it was a petition, they would have had to take the names on the petition and forge these names onto registration cards.
Since party affiliation doesn't mean anything on the voter card except for voting in a primary which was probably already settled by the time of the petition scheme, the reason they checked "Republican" was to redirect the accusing finger at the Republicans.