Is this possible? I want to make an API call to get orders, add shipment to order, and update product details via an API. Right now it appears that I would need to use the api to login via Oauth every time. I would like to automate syncing this kind of data up without the need to login with a user account.
Yes, it is possible. Use the Token based authentication instad of OAuth, which is not the right choice for your use case anyways.
How it works:
Request a token, using username and password (either customer or admin / API user):
Use the returned token in following requests, using the
Authorization: Bearer <authentication token>
Source and full documentation: http://devdocs.magento.com/guides/v2.0/get-started/authentication/gs-authentication-token.html