No, MIL-spec rods are entirely different than either AWS or nuclear. It's all the same stuff in the can or box, but the MIL-spec has very specific testing requirements that must be performed on each lot of material. For these cored wire, that may also include diffusible hydrogen testing.
Indusco (distributor) is a good idea, as are Tri-Mark, Lincoln and perhaps Select-Arc (mfgs).
HTH