Yes, SEO could help.
No, CF does not need to be promoted by MUD word.

I may be mistaken, but as I remember from my check soem time ago MUD is mostly searched by those, who seeking mud fights by women (huh) and some other stuff. This is easy to verify by using some tool like Wordtracker. I already did it. So, MUD its too common word (just not sure about cap letters, but doubt it changes something).

There are many other words, though. But in CF's case I think SEO is not a primary way of ad.