Yes, it's possible to use the individual-level utilities from CBC (from a hierarchical Bayes or an empirical Bayes estimation) in a latent class cluster algorithm.
A stronger approach would be to download the raw CBC data from Discover-CBC (the raw answers given by respondents and the product combinations shown in each choice task) and submit that file to our Latent Class-MNL Standalone software package. That will use Latent Class-MNL to estimate the utilities and find the segments for any number of classes you specify. (Of course, if you don't have a license to our standalone Latent Class-MNL package, then you'd need to find capabilities using R, or Latent Gold, etc.)
The idea you suggested is a 2-stage latent class segmentation procedure. The idea I suggested is a 1-stage procedure. Statisticians tend to favor 1-stage solutions, since errors in the first stage aren't taken forward as truth in the second stage.
All that said, you'll probably find OK results by doing the procedure you suggested. Given your existing tools and given your aims, it could be fine. Just make sure to submit the "zero-centered diffs" (normalized utilities) to your latent class segmentation routine--not the raw utilities. The normalized utilities put each respondent on the same (roughly) scaling.