Is there a way to train Doc2Vec on a corpus of docs and be able to take a novel doc and see how similar it is to the trained corpus?

There are many possible approaches:

• using simple similarity measures (e.g. cosine) to compare the new document against every training document.
• train a binary classifier to distinguish the reference documents from "anything else". Requires negative examples, it's usually difficult to have a representative sample.
• Use one-class classification, i.e. train a model using only the reference documents. The model tries to represent this class of documents and considers anything else as negative.
• Could even consider it as a regression problem, i.e. score documents by how similar they are from the reference documents.