A Timelord can regenerate their head after being decapitated.
In the canon prose story "Shadows of Avalon", the Galifreyan secret agent Cavisadoratrelundar is in the process of regenerating a new head (from the neck upwards) after being decapitated. The process only stops after both her hearts are pierced.
The blow connected. Cavis’s head broke from her body. It flew over the
battlements. Mab completed the sweep of her sword. Cavis’ body fell to
its knees. Then collapsed on to its front. Some sort of energy was
streaming from the corpse’s head, swirling about something that was
quickly developing there, as if a new head was swiftly being formed
where the old one had been. Mab stepped forward and stabbed her sword
down twice. Once for where there was a heart, and once for where one
was about to be. The outrush of energy ceased. Cavis lay still.
It should be noted though, that this was a fresh regeneration whereas in the "Christmas Invasion" episode the Doctor only has enough energy to regrow his hand. There's no in-universe explanation of whether regrowing a head requires more energy than a hand but I think we can reasonably assume that it does;
DOCTOR: And now I know what sort of man I am. I'm lucky. Because quite by chance I'm still within the first fifteen hours of my
regeneration cycle, which means I've got just enough residual
cellular energy to do this.
(He grows a new hand.)
In short, my guess is no. He would (probably) have had insufficient energy left 15 hours after regenerating.