It would all depend on the type of greek culture at your campus. At schools where there are no greek living units and greeks have sections or floors of a dorm, then beign an RA probably wouldn't be difficult or have any adverse consequences, but at campuses where the greeks have house where the majority of members live then you are going to have to work extra hard to do both. It's the same situation that anyone who lives out has to deal with, although you are going to have a lot of commitments to your floor that could interfere.
Basically, look at whether you think that you could do both at levels you deem acceptable. If you don't think that you can do all the fraternity events (parties, chapter meetings, commitee meetings, formal dinner and the like) without your RA duties suffering (being a resource for your residents, making door decorations
, RA meetings, and whatever else RA's do) then don't do it. Both are big time commitments that if you don't fill people will be angry at you. And if you can't even fulfill one groups obligations then there is absolutely no reason to do it. You have huge responsibilities to your brothers and your residents.