I introduced my girlfriend into martial arts. Originally foil fencing and then kendo.
It wasn't my intention to get her into kendo, but she watched me doing a class and decided she loved it. She's blended into it all seamlessly, and nothing has suffered for it.
I've been trying to get her to start Aikido on the grounds that its good for the soul, but she just isn't buying it yet.
She says it's not intense enough, but that's because she's never been on the mat.
Were I an instructor, I don't think I'd find it appropriate to date my students willy-nilly. I suppose I'd make an exception if there was someone I was absolutely in love with, but I don't see that coming up.