That would handle the web aspect of things, but would not install the required program files. You need a dedicated or VPS to run the software regardless of what operating system you choose.
Also Centos is the best OS to use unless you have a really big personal preference to run one of the other linux flavors.
One thing to keep in mind is while there are many games out there that run well on linux, there are many that will not run on linux at all. So you may want to plan your boxes out accordingly. Also, from what i have heard (I have not confirmed this myself), some mods out there don't seem to run well on nix.
Just food for thought before laying down your foundation.