Well, from the student's perspective there is a big benefit. It is called substitute teacher! When your teacher is out holding up picket signs, the substitute teacher shows up to fill their place. This means less homework and less work in general for the student. So, yes, there is a definite benefit for the students!
Teacher strikes and labor issues should happen during the summer months so as to prevent any distractions from the educational process. Strikes are simply distractions that have no merit on the value of teaching whatsoever. Who wants to sit in a classroom with a teacher who may or may not have the best interests of the students at heart? Is learning truly a priority if a classroom teacher sends a message that he or she may not be there in the next few days because of a labor dispute? I'm all for teachers making more money, but that can't happen if they choose to walk out on the very students they vowed to protect.