Strat-
In my opinion ,Yes-- here is the trail
Under D14.1-97 ( I don't have the 2005 spec but usually this item wouldn't change)
Per 7.3.1 "All welders, welding operators and tack welders to be employed under this specification shall have been qualified by test as prescribed in Parts C,D and E respectively of this section or by the latest edition of ANSI/AWS B2.1"

On to B2.1-2005
Per 3.1.3 " Personnal currently qualified by the employer to meet the requirements of other codes or specifications are considered qualified under AWS B2.1 provided the basis of their qualification meets all the requirements of this specification"

Note:There is more to each of these statements regarding conformance to any variables in each individual code/spec.

D14.1 has items that are specific to that specification and are generally listed as variables in section 7.5.2 -Limitations of Variables, so the WPS's that are followed while doing D14.1 work will be specific to D14.1 and usually are very similiar to D1.1 but could contain some variables that make D14.1 different than D1.1.  B2.1 has variables in 3.6- Performance Variables, that are specific to B2.1  Welder qualification are usually the same exact test between a lot of code/specifications but WPS specifications will vary somewhat. So it is critical to find the differences in variables when you have welder qualifications from one code/specification accepted to use on another code/specification. Along with defining any differences you should have the engineer and/or customer acceptance of D1.1 welder qualification  for D14.1 work in writing so that there is no confusion or debates after the completion of any work.

You need to get a D14.1 and compare it to D1.1 which I haven't done to define the differences. Usually these are not a big difference but enough to make each of these code/specifications a reason to be "stand alone" code/specs. The welder qualifications are usually the same but the Welding Procedure Specifications (WPS's)  will usually be different.

Possibly AWS could help with this if one of the people there has that comparison info.  800-4439353 Technical for D1.1 and D14.1

Ken K