It would be possible to create a Nyquist plug-in that can read data from an exported label track, but as far as I’m aware such a plug-in has not yet been written. Unfortunately plug-ins are not currently able to read label tracks directly.
There may be easier approaches.
Have you tried the Beat Per Minute labels plug-in?
If you can create a Click Track that matches the music, then you can create the labels using “Beat Per Minute labels” with the same tempo and the same starting point as the click track.