I would think that you want some overlap. Even a really good crossover won't simply "cut-off" at 120hz exactly. The question is what will cause worse sound, a little overlap or a gap in frequencies?
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It seems like what you describe would work... so your description is puzzling. However, even if this would work, it would hardly be worth the sonic degradation on your system. The quality of the sub-crossover is probably low, and it would rob a lot from the signal feeding your power amp.. and affect the quality of the sound from your main speaker.
I had this dilema once with NHT super zeros and a sub, where I opted for making simple passive high pass filters in line between the pre and the power amp, resulting in much better sound than using the Sub crossover. I still have these sitting arround, and would be happy to pass them on to you for free. However, the Impeadance of your poweramp would determine if you could use them or not. The cut of is about 127Hz when used with 38Khoms impeadance (ROTEL), but would change depending on the impeadance of your amp.
Does your CT-120 provide speaker-level in/out connections? If your pre-amp or integrated amp is meant for stereo only (no processor) and/or lacks an output labeled "subwoofer" or similar (which are usually filtered) you may get a better result using the high-level (speaker-level) connections to the sub in your case. It sounds counter-intuitive, but connecting a powered sub this way can actually sound a lot better if your preamp or integrated is not fitted with a line-level sub output.
Also, the "line out" on many powered subs is often not meant to feed a signal back to the pre-amp, but may be used to "daisy-chain" another sub. That may explain why you are not getting any sound from your main speakers with it connected this way.
Try running speaker cable from your preamp to the sub's speaker level inputs, then another set to your monitors from the sub's speaker outputs (assuming it has this connection, of course), and the adjustable crossover in the Velodyne will filter out the low frequencies before they reach your monitors so they will play louder and cleaner than otherwise. Definately worth a try! JZ