The Doctor's plan to save Gallifrey and destroy the Daleks is as follows:
DOCTOR 10: The Daleks would be firing on each other. They'd destroy themselves in their own crossfire.
WARRIOR: Gallifrey would be gone, the Daleks would be destroyed, and it would look to the rest of the universe as if they'd annihilated each other.
To my mind the Daleks would stop firing pretty quickly when they realised Gallifrey was gone. So how would they destroy each other?
I could accept the Dalek fleet sustaining significant damage in the ensuing chaos. But with shields, and given their sheer numbers, it seems more likely to me that many would survive.