In the latest NIN Access, Trent Reznor explains how he was involved with the Doom 3 project:
john carmack and i had established a friendship while working on quake. he came to see up playing during the last tour and wanted to get my feelings on a remake of doom with a new advanced engine he was working on. we discussed how cool it would be to create a place that was immersive to the point it wouldn't need a "soundtrack" -- the technology was advanced enough to visually and aurally to create a rich environment you could truly explore and inhabit. we discussed my involvement as the overall sound producer -- from foley and voice over to ambient world noise.
later, i started work on what would be used at the e3 show 2 years ago. it was exciting working in a totally new way with new tools. i was working directly in the game editor and with the programmers refining the sound code and helping the environment come alive. tried "tuning" various environmental sound sources so they'd cohesively interact with on another in a "musical" way. the advanced technology provided enough horsepower to give me a seemingly limitless amount of freedom. it was a lot of work, a lot of thinking in a different way, and a lot of fun. i was working with the best guys in the field -- true geniuses.
our idea was to have no music, apart from a main theme i'd write for the intro. no rock, nothing current sounding, nothing to date the game.
well... eventually time and money and bad management came into play and it didn't work out. disappointing on a number of levels for me, but that's the way it went.
I have seen the engine at work and it is great. i'm looking forward to seeing what they've done with the game.
and i guess tool did the theme song.
This doesn't really answer the question as to how much of Reznor's work might be remaining in the final product, if any.
Update: Note that the "Doom 3 Theme" was created by Chris Vrenna and Clint Walsh. Chris Vrenna was a founding member of Nine Inch Nails and has released a couple of albums under the name Tweaker. Here's a link to a press release, but it might be broken because I wasn't able to access it.