Is it possible to use the armadillo math library in UE4?

MSVC, GCC and Clang all support #pragma push_macro/pop_macro, which means you can just push the check macro before including Armadillo, and pop it afterwards:

#ifdef check
#    pragma push_macro("check")
#    undef check
#    include <armadillo>
#    pragma pop_macro("check")
#else
#    include <armadillo>
#endif