Non-official copies of the game doesn't establish connections to the official gameservers.
And they can't play SP anymore either without some sort of hack. I wouldn't count those players as "part of the singleplayer community".
That is wrong. You can install bf2 and play sp or coop without any internet connection. All you need is a CD key valid for the installer, then you use an offline account ingame to play sp or coop. It does not check if your game or account is valid. You can even run a server (not public) and play in LAN with your friends.
Only when you try to join a public internet server from the ingame list, you need a online account and gamespy will check if your cd key is valid (bought) and not in use already. But since fh2 uses its own gamespy backend, any cd key in the correct format is considered valid.
Since EA chose to shutdown their backend, we can no more differentiate between bought or generated keys. As far as I am concerned, players count. We are not the EA police.