If I don't join a team does that mean I can't go any further in the game?

I don’t believe you have to. Some of the top players are listed as having no team. You can also join a team, leave, change teams, etc.

I’m not at the end of the levels but I don’t think it impacts your ability to play. (That said, I didn’t join a team for like 2 years, but when I finally did it was useful for getting a lot more coins easily, banking free lives, and occasionally getting a nice chunk of diamonds from winning a tournament. If you choose that route, pick an active team that encourages regularly requesting/giving lives and participating in the tournaments. (Free, by the way.))