Just so I'm clear on what the OP question is - do you mean an overall 3DS Smashboards team to represent the site as a whole in online tournaments, or do you mean just a Smashboards online tournament scene in general, where everyone makes their own teams?
Because I actually don't like the former idea. Firstly, it assumes that there would be other sites with dedicated teams to go up against. Secondly, it's closed off.
I believe individual members setting up their own teams and then trying to make a scene out of that would be much better and be healthier for an online tournament scene. Having "the Smashboards team" is demotivating, and sets a definite, constant ranking of who the best players on the site are. Even if that's not the intention of the team, and even if those players aren't necessarily the best 3DS players on Smashboards, they will inevitably be perceived this way. This in turn will demotivate a lot of people, because in their mind, the Smashboards 3DS Team will be the players they can never top, no matter how well they play. So being the top player will feel impossible to anyone outside of that team.
However, we could hold an annual thing or something where Smashboards players go against players of other big sites or organisations, provided the scene gets big enough. This would be done by re-forming a new team every year, which could be decided based on the players who perform the best in tournaments officially recognised by Smashboards every single year. It gives every individual player a chance to shine in the spotlight, but doesn't set a constant, near impossible to beat bar for people to never be able to beat.