Does Rocksmith pick up a guitar with a humbucker better?

In my experience Rocksmith does benefit from a humbucker. This is simply due to the reason mentioned in joshbuhler's answer - the more volume, the better. Since the average humbucker has a higher output than the average single coil, it works a bit better. Another thing I've noticed is that Rocksmith works better with a brighter pickup. For instance, on an LP-type guitar the bridge pickup seems to work better. When using the neck pickup, Rocksmith tends to have problems with detecting notes on the higher strings, especially when playing chords, even with the volume and tone knobs cranked.

So my order of preference for pickups to use with Rocksmith, all other things being equal, would be:

1. Bridge humbucker
2. Bridge single coil
3. Neck single coil
4. Neck humbucker

Everything depends on the actual guitar and pickups, though. Neck humbucker on a bright-sounding guitar might be better than the bridge humbucker on a Les Paul, and high-output single coils (like P90s) might be better than any humbucker. I'm currently playing Rocksmith with a telecaster that has a 10k single coil in the bridge, and it works like a charm. Even better if I switch the neck pickup in series with it.

In the end, you just have to experiment with your guitar(s) and pickups and see which combo works best for you.

One thing to try if you just cannot get Rocksmith to detect notes properly with your guitar, would be to put a booster or compressor pedal between the guitar and the Real Tone cable. I know the game warns you not to do that, but I don't see the harm in putting something there that can help bring the levels up a bit. At least theoretically. I might try it out later and see what happens.

I've found that it seems to depend more on the output volume of the guitar and less on the type of pickup. I've played with 4-5 different guitars, all with different combos of pickups, and the only thing that really seems to matter to Rocksmith is the volume of the guitar. If I crank the volume and tone knobs I get a lot better gameplay experience than I do with the volume at a more normal level.