Yes, D1.6 addresses this.

D1.1:2002 Paragraph 1.2 Limitations, This code is not intended for the following: (4) Basemetals other than carbon or low-alloy steels. D1.6 Structural Welding Code - Stainless Steel, should be used for welding Stainless Steel Structures. Whenever contract documents specify AWS D1.1 for welding stainless steel, the requirements of AWS D1.6 should apply.

One main concern is the difference in coefficients of expansion and if the joint is not designed properly to accomadate this, it will most likely crack. You will need to do a PQR to qualify the WPS, as this would not fall under the prequalified base metals in Table 3.2. Table 4.1 shows the WPS qualification variables required. Don't forget that the welder that welds the PQR test plate won't need to be tested because he will be qualified by passing the PQR tests(see 4.7.4). All the other welders will need to test to the new WPS though.
John Wright