I wouldn't put The Doctor in the Eva-Verse, Rebuild or otherwise. He likes humanity VERY MUCH. The Angels'd last no longer than a 2-parter because he'd find a way to make their existence moot and their drive null. He'd hurt a lot doing it, of course, but the Children of Adam couldn't pick a worse foe if the 9th, 10th or even the 8th Doctors come around.
Neon Tardis Evangelion said:
'I AM STRENGTH. I AM VENGEANCE. I AM ZERUEL.'
'The Doctor. Here for ten o'clock tea.'
'The Doctor. Here for ten o'clock tea.'