Referencing AWS D1.6 para 4.7.5 Base Metal
The base metal used shall comply with 1.2. Qualification established with any one of these base metals shall be considered as qualification to weld any one of the base metals permitted by this code. For all types of welded joints, the length of the weld and dimensions of the base metal shall provide sufficient material for the test specimens required by this code. With the approval of the Engineer, performance qualification test coupons may be with any of the steels listed in AWS D1.1, Groups I or II. Qualification established with any one of these base metals shall be considered a qualification to weld any of the base metals permitted by this code.

My interpretation is that you may use any of the base metals of D1.1 (performance qualification test coupons) which are carbon to qualify your welder with a stainless steel filler metal (with approval of the Engineer).Like ASME, if stainless steel coupons are not available, the welder may use a carbon coupon, purge it, and use a stainless steel GTAW wire to qualify for a stainless steel (performance) qualification.The last sentence states,...."weld any of the base metals permitted by this code." I take it that this code is D1.6, not D1.1, correct?

That is correct, it refers to AWS D1.6