The Oxford dictionary says no, but I have heard the word, and it is readily comprehensible. I would use it. I am surprised it is not in the dictionary.
"During the Outward Bound expedition, one of my groupmates was seriously injured." If you used "teammate," you are implying that you consider the group to be a team, and maybe you don't think that. Blair's suggestion "fellow group members" strikes me as awkward.
Maybe the mavens would want you to spell it "group-mate" or "group mate." As it is one concept, I think it is best spelled like you did.
Don't use on the TOEFL.
I am a liberal, and I believe that language is made by people speaking it. So, I guess, no, the dictionary says it is not an official word, but I think it should be.
Sorry I answered the question twice. "comments" removes all of the formatting.