Sure, but in recent games you also wouldn't talk about having "your own server" or joining "a server" - you're joining a match or a world or similar. You might refer to "the game's servers" if they happen to be down or overloaded or something, but it's less common these days to talk about a specific server.
The exception, of course, being games for which it is actually still possible to run your own servers. Minecraft comes to mind.
