Its a BLAS library standard API that you are linking to, so the vendor doesn't matter so much (in theory). In practice, the amount of annoyance that you have to go through so that it links correctly can vary a lot. Even MKL did not implement all of BLAS / Lapack and that would lead to some linking errors.
I know that BLAS is a standard API, I switch between BLAS implementations fairly often :). I suspected that Eigen relied on some non-BLAS functions in MKL, since they explicitly state that only MKL works.
Re GCC, the same here. ICC is mighty expensive.