The BTB opens at GS interception. You have a different model 737?
I guess I do latetonite, my BTB's are open most of the time but in this scenario they will be closed. My Cross Tie Relay does tend to fly open on G/S capture though.
My thinking is that if you're operating on one IDG and your APU is u/s, both transfer busses will be powered, they in turn will be powering your DC busses through the rectifiers both before, and after glide slope capture. You will of course have lost a lot of redundancy and protection, but I still see no reason why it wouldn't work.
Don't interpret that as me thinking it's a good idea, if a divert was not an option I think I'd rather do it manually on a protected ILS. Good conversation though.....why do I get the feeling I'm about to learn something?