Interesting question.
The Intel MKL will speed up any BLAS operations, e.g. matrix multiplication, cholesky decomposition, etc. So solve() might run faster, but optim() probably won't (depending on what you're trying to optimise). One would think that lm() also falls into this category, but the lm() code does not call out to any BLAS functions, so it will be the same speed.
The foreach package does not have a parallel backend for Xeon Phi, as far as I know.
I hope this helps.
Good luck with your project!
Andrie