Depends how they do it—given a game is running locally, they don't need to connect elsewhere to get ads. They could easily bundle a load of ads with the game installation. In this case, it would need game mods, and they're not gonna be the kind of mods EA will ignore, they will actively combat it.
If they do function like a regular ad platform and fetch ads as they're needed, something like pihole will be able to block it.