Not at all Students would abuse the system and try to get any teacher they don't like fired. It happens all the time even without and actual system in place. It wouldn't work at all, but especially not if it was an anonymous poll. That would result in students getting ALL the teachers fired in an attempt to get out of classes or to prove a point.
Yes, he was already invited Even if she doesn't want him to come, she already invited him and you can not really retract an invitation like that. Not letting him come would merely show weakness; she doesn't agree with him and would rather just ban him. She shouldn't back down due to pressure of random people.