Would Microsoft have crushed Sony if the Xbox 360 had had HD DVD built in?

[S.T.A.G.E.]

HD-DVD was already beating Blu Ray before Sony interfered in the format wars with the PS3. Hypothetically it would've wounded Microsoft as much as Sony, but HD-DVD still would've won. In reality Microsoft saw no need to focus on DVD players when they wanted the head start to acquire all of the games.