He is just one guy in a vast universe.
Perhaps one nice city's crime is reduced slightly, but that is a out it.
Even if he started working for the Imperium there will be just one of him
He can only reduce the crime slightly in one city?
Metropolis in most iterations is a pretty awesome place to live and the only reason Superman is so busy on DC Earth is because it's DC Earth. There's literally thousands of metahumans on there and wild tech ranging from LexCorp to Intergang and yet Superman still has time to do Justice League things and have numerous adventures in SPAAAAAACE which leave considerable impact on galactic affairs until the eventual comic book reset/retcon.
Stating he's just one guy in a vast universe belies several important points.
Lots of people in 40K who are known far and wide are literally just one guy and yet have made impact in this vast galaxy. Also its a galaxy, not a universe. Superman has probably been to more galaxies then we've seen in Warhammer 40K but that's besides the point. And Superman is directly more individually powerful then pretty much anyone in the Warhammer 40K setting in its past or present.
So reducing one
nice cities crime is just hilarious downplaying from someone who has Stage One understanding and analysis of Superman.
If he's independent though, I do think his effects would be mitigated. I'm not sure most incarnations are into empire building but it could be something that occurs inadvertently if he adopts some certain sector or part of space as his own to protect. Kind of like how he'll work with other heros (ala the Justice League) and cooperates with the United States government, Metropolis Police and Green Lantern Corps or Starr Labs, the New Gods etc.
His best bet when it comes to working with the Imperium would be aligning with some Rogue Trader or Radical Inquisitor, then he can do more impactful things... like smashing Tyranid splinter fleets and Ork Hordes or the like. Superman may not like the Imperium of Man, but he also takes a pretty hard stance on genocide and mass murder of (less then) innocents still.