No he did. There’s a whole series of Eight audio books that I’m pretty sure are considere canon. I’ve never read/listened to them myself, but a shit ton of my tumblr friends have and I’ve seen their liveblogging, and Eight definitely experiences the Time War in them. If I’m not mistaken, he was the one that made the choice to time lock Gallifrey.
Because of above. If I understand the implications of John Hurts doctor, he will technically be ‘nine’ and was forgotten because of his choices in the Time War and Eccleston would have really been Ten, and Tennant was Eleven, and Smith is Twelve.