I think that the greater question is "Will the TARDIS allow The Doctor to die?" We've already seen that the TARDIS has regenerative power through it's power source; it even managed to make Captain Jack nearly immortal.
I think it's a symbiotic relationship at this point. The TARDIS will keep The Doctor alive as long as The Doctor keeps the TARDIS alive.
That works too, I've love it if the TARDIS has stored up so much Arctron Energy through her travels that she can grant an undisclosed number of Regenerations...Doctor 13 says goodbye to her as he lays down for the final sleep, and she brings him back...and Ginger
One Day I hope to be the Man my Cat thinks I am
Where are we going? And why are we in this Handbasket?