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.

Conservation of momentum dictates that proton and electron will move away from each other. The decay energy might be absorbed by a nearby nucleus in an medium to a large part, leaving only a small momentum for both particles so they can form an atom, but usually it won't. In the average low-density case, the proton and electron will find other partners only after quite some cooldown.

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.