I didn't look back in D1.1:2004 at Table 4.11 which deals with the essential variables requiring recertification of welders, but in D1.1:2006 (and I don't think it has changed from previous years) the Table was renumbered to say Table 4.12 and gas/no gas is not an essential variable unless I've missed it. So with that said, Yes if the welder qualified on FCAW-gas shielded they are still qualified to weld with FCAW-self shielded and visa versa.
Fran, I agree with part of your statement because these two are different due to the essential variables for requalification of the (WPS)welding procedure(see Table 4.5(3)&(19)...but not for the welder, again, unless I missed something.