Not really. In FLUKA, low-energy (< 20 MeV) neutron cross sections come from external libraries, featuring a dedicated treatment, and that’s why the manual focuses more extensively on them. Nevertheless, cross sections for all other kinds of particles are included in the code, which calculates them internally.
Of course, if certain cross sections are not included in a code, the latter cannot properly treat the respective processes. But, as pointed out above, the assumption that FLUKA misses charged particle cross sections is orthogonal to reality.