I don't know the song you're talking about, but mostly pedal steel is played through clean amps, often solid state even. Probably some compression on it, maybe a hint of delay and/or verb. Not much else. Sometimes phase shifter I've heard. Occasionally a drive pedal, but mostly clean with a little bit of ambience and compression. When watching steel players, it becomes clear that the huge majority of their sound is coming through the instrument and hands. Not a lot of external processing.
On the other hand, it's Lanois, so who knows what all he might have put on there. Lanois seems like an Axe candidate if ever there was one. He creates some of the most gorgeous blend of "real" beautiful instruments/amps with digital time-based processing of anyone who ever lived. Emmylou Harris' Wrecking Ball CD is one of my all time fav discs and it's his production that takes it to a place she's never gone before. He's made some of the biggest selling recordings of a bunch of bands he's produced because he really knows how to take the strengths of an artist and create a fantastic sound context for them. U2, Peter Gabriel, Neville Brothers, Dylan among others all had huge success with him in the studio.