Yes, there is RV parking in Atlanta.  There will be a lot of traffic depending on the time of day but that is to be expected.  You'd have to gauge your own comfort level with that kind of driving to determine if it is a good idea.  But RV-sized vehicles drive in Atlanta all the time in the form of buses, Prevost motorcoaches, school buses, semi-trucks, etc.  Sometimes people here equate "I wouldn't do it" with "It can't be done."
Parking is available at the Georgia World Congress Center (http://www.gwcc.com/)  The most likely place they will let you park is the Marshaling Yard. That is where motorcoach and school bus parking for the Aquarium is directed to on the Aquarium's own website.  I'd call the GCCC before hand and make sure that there are no events that would restrict your access to one of their lots or the yard.  If you are comfortable with your driving abilities and study the route / roads in an out of there I wouldn't hesitate to do it if it suits you.  You can take public transportation or walk from there.