You leave a lot of possibilities open. Cygwin .a files will work with 32-bit Windows, within limits. They won't work with 64-bit windows, as cygwin doesn't support the /machine tag. In our usual usage, we create the .a files from objects built by IVF and MSVC (or ICL). The Microsoft linker throws a warning for each object which has been renamed to .o, and sometimes there is difficulty with correct handling of the differences between C and C++. It would be quite difficult to use .a files generated by g77, gfortran, or g++. gcc might fall in the middle, but you would have to deal with the linkage conventions being different from what is usually expected with gcc. Evidently, you get quickly into areas of non-support.
