well neutrons decay in about 10min (avg) into fresh new protons (plus an electron) so perhaps not
In very rare cases most of the energy might also be carried away by the neutrino that is produced as well, so decay to hydrogen is not impossible in a vacuum.
Hence, there is far too much energy released for the electron to stay bound in essentially any case. If the neutrino carries away all the energy (with momentum conservation soaked up mostly by the recoiling proton), it could re-bind, but that process should be exceedingly rare. In that case, the result would see an (excited, probably) hydrogen atom recoiling away from the invisible neutrino.