The energy release in neutron beta-decay is ~780 keV. This should be compared with the hydrogen binding energy of ~13 eV. Hence, there is far too much energy r

The energy release in neutron beta-decay is ~780 keV. This should be compared with the hydrogen binding energy of ~13 eV. 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.