I love it!! I love the idea!
You could also play a Q (kinda cliche, but it works), an enemy, etc.
We'll have lots of opportunities for guest spots!
Oooooohh - a Q could be very fun! But I also like the idea of either a relative - or someone else of some importance - of one of the "main" characters who shows up occasionally and causes trouble. Perhaps, in much the same way Lwaxana did, by having a massive unrequited crush on a superior officer, causing embarassment all around (except to me, of course!).
The opportunities are endless...