[Saxmusiclover]

I wouldn't worry too much about getting the range right. It's up to the singer to pick a song they can do, they'll only learn what's in their range if they get stuck with some things outside of their range.
Plus: It's not like they'll be in tune anyway. I've got tonedeaf neighbours downstairs with a karaoke machine. Awful.

Rhys,
I used to work in a karaoke bar. If the singer knows the song and can sing it well he/she does it in the original key.
Many people sing off-key and I doubt if the band adjusting to them will help. Also, they don't expect it anyway. (Just imagine how you'll react if the karaoke machine suddenly adjusts it's tune to your singing They'll probably be very surprised or, more likely, they wouldn't care because they're too busy listening to themselves sing and cannot hear the accompaniment too well anyway )
I would suggest you just play it in the original key whether the singer is in tune or not. Makes life simpler for them and you.

Ben