Generally speaking, yes. You can be online in Steam while using mods - indeed, rosters are still distributed through the in-game sharing functionality, with the art packs being downloaded and placed manually - but mods have been known to interfere with online play, causing the game to fail consistency checks. Even small cosmetic mods can be pinged that way and cause connection errors. Ironically, there are people who get away with hacking/cheating online while more innocent mods get caught, but that's a whole other issue.
But yeah, mods are basically for the offline modes. If you did want to play H2H with a friend using a custom roster/heavily-modded game though, there's always
Parsec.