Would bombarding ionized hydrogen gas with neutron radiation cause cold fusion as the neutrons have no electrostatic repulsion to overcome therefore making it much easier to get within range of the strong force?
You don't have to ionize the hydrogen, because the neutrons (to excellent approximation) do not see the electrons. Low-energy neutrons in hydrogen are captured to form deuterium. Because deuterium doesn't have any bound excited states, each capture releases a single 2.2 MeV photon.
In building a practical apparatus, it's important to know that the probability of n-p scattering is much higher in any individual interaction than the probability of capture. This is especially true if the hydrogen is warm or if the neutron energy is above 15 milli-eV, which is the energy of the first rotational excitation of the hydrogen molecule.
Most people who say "cold fusion" are interested in energy production, and are disappointed that there is no stable isotope from which neutrons can be liberated for less than 2.2 MeV. The complete cycle requires substantial energy input.