Yes, you need all three crystals activated to unlock the door, so you probably want to bring in more friends.
3 people: You have to fight both Gurtoks (the ice and the fire) and they will NOT respawn so you can run in that area without getting into a fight. (P.S. They drop those nice level 50+ Athames and Rings which give the best Health and Mana stats of your school plus a 15% power pip chance i believe [correct me if i'm wrong]) and then you can have 3 people activate crystals and one run to the door.
4 people: You don't have to fight Gurtoks, but make a plan so that 1 or 2 person(s) can be "bait" and log out, then quickly port to either of the other 2 people in the Spyre.