Add CRM contacts to "groups" that would have access to forums?

Add CRM contacts to "groups" that would have access to forums?

We are evaluating if we want to migrate from a web-based forum to using the Desk/Community forums for our customers.  We have ~3,000 customers that ask each other questions across a number of topics.
But as they are our customers, we won't be making the forums accessible to non-customers.  Is there a way to assign groups to contacts based on a field or value within the CRM?
Ideally, anyone we set as a customer in the CRM would be automatically within the customer user group within the forums.