It really depends on your definition of "team".
Some competition organizers automatically consider a school a team, and they will give team trophies to the school or gym with the most points in the tourney.
Some organizers will dictate a minimum and maximum number of competitors by weight, skill level, gender, etc. to be eligible for team scoring.
There are tons of variations on how teams are defined - It really depends on the sanctioning body or host of a tournament as to whether any given group can be considered a "team".
I guess casually any group of "fighters" with matching t-shirts could call themselves a team if they wanted to...but not every sanctioning body would consider them legitimate.