No, it isn't. Imperium has nothing to do with either Nazis or Soviet Union beyond pure superficialities. It has some elements of Nazism, but organizationally, it is really "Holy Roman Empire IN SPEHSS!". Imperium is essentially a feudal state, and it is in fact much better representation of feudalism than most fantasy feudal societies. Planets have high levels of autonomy, and Imperium as such is essentially an alliance of autonomous planets and several major organizations (such as Adeptus Astra, Adeptus Mechanicus etc.). These organizations own planets of their own, and are basically states-within-a-state. They are not the only such internal-states - most notably there is Realm of Ultramar, which is basically Roboute Guilliman's personal fief. Planets which are not members of one of said organizations are directly members of Imperium of Man - and these planets enjoy a very high degree of autonomy. Basically, policy of Imperium is "pay the tithes, send psykers when Black Ships come, and don't make me come over there". Other than that, each world can have governmental, cultural, social and legal order of its own choosing.
Honestly, if it weren't for various space horrors and necessities of combating those, it could be said that IoM is much less authoritarian and intrusive than, say, United Federation of Planets or Galactic Republic.