So far, I've not found a way to have the Steam Overlay inject into GOG's Battlefront 2. Adding GOG Galaxy as a non-Steam game doesn't work, adding the actual game .exe as a non-Steam didn't work, nor did that method with a .vbs script. The game launches, but no overlay.

So how do we get it? All my buds are on Steam, so having Steam overlay support is pretty important.

Have you tried Global Steam Controller (GloSC)?

That's a funky looking site. It also wants to install a driver. Eeeeeh.

I'll give it a go, see if it does anything.

Edit: That program requires the game to be in borderless windowed mode. Battlefront 2 doesn't even have normal windowed mode.
So it turns out that we don't need to launch the game through GOG Galaxy. The multiplayer is integrated into the game's executable, so just adding BattlefrontII.exe to Steam works just fine.

Colour me surprised.

... and where else would you possibly expect Multiplayer code to be, if not in the .EXE of the game?
The Galaxy client is just a fancy skinned way to manage your games with access to the GoG shop. And chat.

In the wrappers of the community software. For example, Dark Souls 1.