Try using Sound Forge\'s Noise Reduction, and take the verb tail as a noise print.
You\'ll get all sorts of phasing artifacts if you\'re not carefull, but if you use it careffuly it will help just a bit.
But don\'t expect to get a warm close miced sound out of ambient recording.
The NR trick will help just a bit, but basically you are right. The answer is probably no, especially on a voiceover.
This is why voiceover rooms are some of the quietest rooms around. The human voice, even at close range, will dip into the \"noise floor\" of just about any normal room, and therefore, you\'re amplifying a LOT of noise. As lex mentions, you can try NR, but in general using enough NR to clean up the noise really distorts the program that dips into the noise (which is extensive in a voiceover).
Tough problem. You may want to go to a local studio and re-track the VO rather than deal with the compromises.