Judging by the fact that you recommend shadowing, is it possible to assume that their team may have financial difficulty?
To give them the best opportunities, if finance allows it, would be to let them start a team, and learn from the difficulty of those time-crunched hours. As a mentor team, you can help them so much by training them (both students and teachers) in robotics and the principles of design and strategy.
Attend kickoff together, if possible, and let them be their own team with their own number and identity. If they aren't able to get sponsorship, your shadow idea is spectacular. Just keep in mind, that the strongest mentor team is the one that can give a rookie team the resources to thrive on its own: providing those resources should be your priority if you choose to take a team under your wing.

This way, in the future, there will be a local area team that you can collaborate with both socially, technologically, and in projects.