You might have a grand jangling around in your pocket

It seems like you should just try it and see what happens. My assumption is that they will connect to the servers and work without any issues. I've seen a video of how someone does it on steam. I'm not sure about GOG but it could be similar. According to some users on steam it's really easy to connect the games together. It's DRM free so you should be good to go. Let me know if this answer is helpful.