Hey there! Small disclaimer: I'm just trying to give my opinion and advice and hopefully not offend you. If I do, sorry 'bout that.
In my experience, marketing is an essential part of any game development team, but a marketing degree... maybe no?
"Triple A" games will double their budget just in advertising but will sometimes outsource the advert work to a firm. If you want to do marketing for games, maybe look to join a good firm in a city with a strong game dev industry like Seattle? But this path probably won't get you into a studio to make games very quickly.
"Indie" games and studios tend to work on a shoe-string budget when it comes to advertising; usually having the game artist(s) double as a promo-artist(s) and everyone on the team running around the internet to show off their game. If this is where you wanna be, then do as much art work for indie teams as you can. Get stuff done and get paid!
So it really depends on where you want to be, but when it comes to a marketing or even an art degree; the degree itself just means that you understand the meaning behind what you're doing and you've been able to tough out some book learnin'. What's really important is a highly polished portfolio with creative ideas, original work, and some previously published works. You need to show you can do what your degree suggests you can do; to show that you have been able to put your education into action and that you have the skills needed. Because that's a big part of it. You need skill and knowledge. Knowledge is something anyone can get where as skill takes a boat-load of time and practice, some innate ability or leaning toward the subject, and then some more time and practice.
Also, avoid fan-art like a plague. When I see fan art, I think "great, this kid can copy what they see." It doesn't show skill to copy a design and if you can't show skill, then you won't get hired. When you're drawing fan-art in their original style, what does that really show potential employers? Only that you aren't creative enough to come up with your own ideas. Sure, once you get to be more recognized, you can draw your take on others characters and show them off, but if I were you, I would definitely avoid drawing in other peoples style.
But those are just my suggestions...
Good luck with whatever you decide to do.