First off, yes, it is possible to create a multiplayer roguelike using a MySQL database. While the others here said that using this database as your server is a bad idea, I will only say that it is PROBABLY a bad idea. It depends on what you're trying to accomplish, exactly.
I wouldn't use a MySQL database as a server for a game that I am planning on distributing for public consumption. As the others said, the performance of the database will not be good. If many people began playing the game at the same time, it is unlikely that your database would be able to perform. Think about this: when one player makes a move, the other players need to be notified somehow. The only way they can be notified is by reading from the database. So they will each have to continually run select statements on the database, looking to see if any other player has inserted his move. Lots of players all running select continuous selects will bog down the database.
If you want to use the database as your server, your game should meet the following criteria. First, you should be trying to create a sample game to play between you and your friends, where you expect a handful of people to be playing at one time. Second, the game should not require anything near real-time updates between players. For example, if players can only act on their own turn, then it may not matter if players have to wait a few seconds in order to detect that a player has finished his turn.
If your game meets these criteria, then you may want to give it a shot. Using a MySQL database as your server is the flat-out wrong tool for the job. However, it is a tool that you know. In programming, it is common to run into technology barriers: you want to create something, but you have tons of learning to do in order to do it the right way. This can be discouraging. In my opinion, while using the wrong tool is less than ideal, it is better than not programming anything at all.
If you want to try a server, then you'll need to understand where and how your server will exist. Does it run on a computer you own? Do you have some webspace you can run it on? What technologies are supported there? Perhaps your server can run in the same place as your MySQL database.
I also think that creating a server is not as hard as it sounds. If you provide details about where you might be able to run the server and how your game will work (does everyone connect to the same server and play in the same world, like an MMO, or are there multiple game worlds running at a time? Do players all take turns, or is the world moving in real-time?), then maybe I can help you walk through the process of picking technologies and getting a basic server setup.
