Once the soul is ripped, it's sealed forever.
Orochimaru took back the hokage's souls and his limbs so its not forever. If Izanagi was activated first, it should trick the death reaper into thinking he already collected the soul. It creates a false instance of reality (Izanami forces the caster to admit reality) so it would only be ineffective if the soul was taken before Izanagi was activated. Of course, if you argued that Izanami forces true reality, then Izanagi is still fake, and the soul was already taken.
Orochimaru took back the hokage's souls and his limbs so its not forever. If Izanagi was activated first, it should trick the death reaper into thinking he already collected the soul. It creates a false instance of reality (Izanami forces the caster to admit reality) so it would only be ineffective if the soul was taken before Izanagi was activated. Of course, if you argued that Izanami forces true reality, then Izanagi is still fake, and the soul was already taken.
Dunno... but if izanagi was activated before reaper took soul then there is a good chance...