Yes! You can team up with up to 3 friends to make a team of 4 Fall Guys. You can then all matchmake together.
In the Main Show progress is based on your individual qualification. If one team member is eliminated, they stay eliminated. If you qualify and your friends don't, you can still progress to the next rounds without them. Remember, only one Fall Guy can win... so if it comes down to you vs. your friends... you will have to turn on them!
In shows like Squads your progress is based on the team performance! You may not all finish a round, but if you score enough points together you can still progress.