Is it possible to access audit logs through the API?

You can look up the comments for an item using the call: /api/cm/:itemtype/:itemid/logs

This call will return the information for a specific item - you'll just need to change out :itemtype to indicate if it is for courses, programs, etc and change the :itemid to the ID for the item you'd like to see the audit log for. Once you have made the call, your information will be returned in JSON format.