Hello Danit,
We do not have experience with sound to time code conversion, using a BPM analyzer. We are also not familiar with the devices that you have found. However looking at the websites. The USAMO seems to support some MIDI messages which the CueCore2 supports as well. Therefore there is a change that they can work together. But I can not guarantee this.
A second problem you may find is that there is a limit of 128 tracks in the CueCore2. Which may not be enough if you want to jump to the next cue every beat of the music. A track is a sequence of frames. Every frame can have its own light effect. However you can not "manually" step trough the individual frames.
However if you can run time code with your audio. You can use actual time code which allows you to run a track which is synchronized with your audio. If you can get your audio setup to send SMPTE, MTC or Art-Net time code.
Something that may interest you is SMPTE which is time code in an audio signal. Which you may be able to play on a different channel from your audio setup.
Best regards,
Guido