It would have been much less likely, but not impossible. (this is in response to extra dry, above)
If AH had been removed in 1938, say, you would still have all the apparatus for rearmament that had been built up in the previous five years; as Napoleon said, you can do anything with bayonets except sit on them.
That went along with a continuing social crisis that the rearmament plan hadn't really dealt with. I'm reading Tooze's economic history of the Reich now, and not only is it excellent, it goes into detail about how the living standards of the masses in general and the urban working class in particular were not lifted by much if at all in the six years before the war. Hence the conquest and the consequent looting of occupied territories. The idea that Germany needed a strong military state to build up its economy and win 'living space' in the east was around for a good long time before Hitler as well.