Can Google Speech API speaker diarization label a common speaker across multiple audio files?

Question

Suppose I had individual call recordings of calls to a help desk. Typically, a call will involve a member of the help desk from a small known pool of people, and a much larger group of people calling in. I am able to use the call diarization features of the Google Speech API to transcribe these calls, and then separate them into channels that are specific to the individual speakers on the call. I'd like to start labeling these channels identifying help desk workers and others. While I can approach this heuristically, I was wondering if the API could do this for me.

I haven't tried anything yet, beyond successfully performing speech diarization on individual calls.