It could work but it depends if there is a need for him to join them. It would have to naturally happen and well he never met xavier just saw the kids go to him. He had no interaction with any of the kids either so the chances of Gambit seeking out Xavier would have to be a real good reason.
I've thought about possible team variations i think the best one we could do for x-men first class is...and i think another key factor in it is the story, is X-Men First Class a story about how Xavier and Magneto were friends then fell apart thus splitting the school to form there own band of mutant teams.
If this is the case this is how i would see it...
Xavier & Lenshire's school for the gifted
> Professor X
> Magneto
> Beast (Pre-Blue Fur)
> Young Cyclops
> Young Jean Grey
> Young Storm
> Young Mastermind (Jason Stryker)
> Young Mystique
> Young Toad
During the corse of the movie, maybe Magneto realising he and xavier's ideas differ. He uses a fragile minded Jason Stryker to aid him, to convince others in there school that Magneto's way is right. It doesnt work on Mystique but she is just generally agree's with Magneto's idea but Toad is convinced. Forming the brotherhood, Xavier realises that he has had a hand in there formation and so creates the X-Men to counterbalance it.
I dont see a need for Gambit in the film, Judging by what i was told his role in the movie is, i think it was something to do with he was a mutant that escaped strykers base and wolverine seeks him out to find the location. But i havent seen the leaked film so i dont know if he is any other scenes or there is more to his story. But personally a mutant that is locked up by stryker and i'm guessing tortured the only person who could relate is Magneto...
So if Gambit is in the movie, im guessing Magneto had something to offer him. Otherwise i dont see any reason for him to be there.