Absolutely you can, but I strongly urge you to get your own liability insurance. Most of the teachers I know joined the union for one reason only: 1 million dollars in liability coverage that they couldn't afford otherwise. Only fools teach without such coverage- you can get sued for making eye contact with a kid these days.
Teachers who want to belong to a Professional Education Association should consider joining the Association of American Educators (www.aaeteachers.org) instead of the Nation Education Association Union. The AAE offers excellent Liability Insurance.