@cc2 is correct, you can include any existing default or custom property when creating contacts using the Contacts API. You can create up to 1000 different custom properties per portal, as well.
What other properties can be added to a Contact through the Contacts API?
Where can I find a list of all those default properties though?
Also, just some more context: I'm creating an API call to bring in information from the Azure Marketplace so that the form on that site uses the Contacts API to pass that information to our HS instance. Should I be using the Contacts API or the Form API?
The Contacts API seems to mostly work fine, I just need a property where I can track the channel/source of the contact.