You can re-use the requests.Session() object of a RoboBrowser object to do your own POSTs with the same cookies:
response = browser.session.post(...)
The RoboBrowser state won't be updated though; you'd have to pass the response object to the RoboBrowser._update_state() method.
browser._update_state(response)
For AJAX requests you wouldn't need to do this, however.
Take into account that future versions of the library may change how that works; it's not a documented method.
However, normally you'd post to a site because you are handling a form submit; leave that to the provided library functionality (RoboBrowser.get_form(), then RoboBrowser.submit_form()).