I’m fairly certain that what we hear on the record is cut from a much longer recording and it maintains some granular delay and tons of reverb from the parts we do not hear. So I’d say it’s a 100% wet signal that we are hearing the long tails of. Then the foreground melody is also heavily processed very likely through a modulation model we sorts. The Line 6 MM4 can emulate a Leslie speaker (the one where the cone spins around) and something like that could get you there once you have the tambre of the ‘organ’ patch in hand. Remember that Trent Reznor is extremely experimental so if that melody was made with samples of the reverb tails of the whole textural background in key and then put through a resonant filter that would not be out of character for him at all.