As others have mentioned, it does appear as if Batman existed in the Smallville universe, given that Chloe alluded to him and Wonder Woman, plus at least one character (possibly more) mentioned Gotham. This means Batman's existence didn't really affect Clark's life.

Given the fact Batman existed but had no traceable influence on Clark's life, I assumed this meant Gotham was pretty far away from Metropolis. I also figured this meant it was safe to say there were notable superheroes in other major cities, which made the national Vigilante Act thing seem more realistic given the unidentified superheroes were a "problem" in places besides Metropolis.

Now what if Batman was part of the Justice League? I don't know if I necessarily would say Oliver filled in Batman's place, but I do agree that Batman being in the league would diminish Oliver's role. Besides Clark, Oliver was really the only major character in the League, and I think if the show had had Batman, Batman would've had the place of the major League character, and Oliver probably would be about as major of a character as Aquaman or Cyborg.

All that being said, now I'm wondering if they intentionally kept Batman away from being an actual character in Smallville so the spotlight wouldn't accidentally be taken away from Superman. Hmmm.