Long day today, so sorry for the delay. Sleepy, so no promises on quality of replies :p.
Yep, you can still call replicated functions on objects within the GameMode.
If you want that the player on a listen server is always on team1 and the client is always on team2, there are a couple things you could do. The way closest to what you already tried would be to actually check if they are locally controlled or not. The server representation of the listen server player will return as locally controlled, while the server’s representation of the client player will return as not locally controlled.
I don’t remember precisely how we normally do this off the top of my head (would have a better answer when I’m back in the office), but the basic gist is we usually actually create another actor that is set up very similar to how playerstates work that specifically holds info about an individual team instead of an individual player (so we call it something like ATeamInfo), which could potentially also store its list of members if it wanted. We normally have the GameMode spawn the actual team info actors and then I think we keep a list of them on the GameState for easy access by clients if they want to query things. The TeamInfo actor additionally normally would store team-level concepts that could be mode specific. Simple example, if you’re making a capture the flag mode, you could let the CTF team actors store how many flag captures each team has.