If you set up your own autodata in the settings, Beeminder will do a POST with the username and slug, will follow the autodata schedule, and when you click refresh on the goal, it’ll pull new data in. It’s not quite EXACTLY what you asking for, but it might be close enough.
If you go to https://www.beeminder.com/settings/account#account-permissions, Create an App, and then assign a goal to that, it’ll all go together. I usually tie the autodata to the goal using curl, with something like curl -X PUT [https://www.beeminder.com/api/v1/users/USER/goals/GOALNAME](https://www.beeminder.com/api/v1/users/USER/goals/GOALNAME) -d auth_token=REDACTED -d datasource=AUTODATANAME.