Hi @CWills,
Thanks for your question. In the current release it is not possible to save a classifier and re-use it to classify a sample that is "genuinely unknown" — this is planned for a future release, but there are security/format issues that we must resolve first.
If you are familiar with python, this is possible with QIIME2's Artifact API interface. You would train a classifier and then feed in additional samples for classification.
Do you have a specific application in mind? You are welcome to submit a new feature request, though an issue already exists for saving classifiers.
Hope that helps!