Yes. I always hand over the boarding pass with my passport.
I've always gone through immigration before 23:00 too, so don't know what time they change their stamp dates over. I imagine it would happen at midnight.
Conversely, I wonder what would happen if you arrived in the country at, say, 23:00 and took your time going through arrival immigration, waiting till after midnight? It'd probably take that long anyway, with queues, but if you got to the front and kept letting the person behind you go first until midnight, would you gain a day?