Actually I tend to think that the Nazis would have been very interested in Space. But they would have been interested in it in terms of conquest. Nazi ideology needed enemies and war-Jews, Communists, etc. So if they succeeded in becoming the dominant power on Earth, what's next for them, other than to go out into Space looking for aliens to make war upon and conquer?
So it would be more like the mirror universe Terran Empire than the UFP.
It would have been mighty, mighty interesting to see what would have had happened had the Nazis met The Borg.