I don't think other teams, including ours, will think it's cheating. However, besides the point I made earlier, it IS putting all of your eggs in one basket. Seldom can we be sure we've made the right trade-offs during the design process.
148 and 217 got so much grief in 2010 not because they shared the same design but because they built robots so much more advanced than other teams because of their hands-on mentors and IFI partnership. With your commitment to having students do most of the work that wouldn't be a problem for you folks.
We're building four
BunnyBots in our lab right now no two of them the same. The students go out of their way to make them different to have the fun of doing it their own way and to see which design turns out to be the most effective. I think it would be more fun and valuable for the students if they were different, but that's just me.