You do realise that using the Internet at all will use up part of your download limit, right?
Your ISP doesn't actually track things like "web browsing" versus "downloading a file". To them, everything you do -- web browsing, downloading, checking your mail, running a peer-to-peer client, playing any online game, or running any online game server -- is all just "traffic".
So yes, running any game server will use up at least part of your download limit. Actually, it'll use up more of your upload limit than the download one, but it will use up a bit of both. But you're using it up just by accessing these forums, or by playing as a client.
It's all about how much traffic the server generates. That's based on how busy your server is -- more players connected for more time = more usage. And even then, you have to put that in perspective with what your actual download limit is. Running a server for a weekend probably won't use up your limit. Running it for a whole month might. Or it might not. Again, depends on how busy it is, and how high your limit is.