Yes, it's possible. An "On Form Submit" trigger needs to be installed. The function that is associated with the submit event will run every time that the Form is submitted. Both Forms and Sheets have "On Form Submit" trigger capability.
Here is a link to the event objects documentation:
Installable triggers
To make an HTTPS Request the script must be given permission to make an external request. Use:
UrlFetchApp.fetch(url, options)
to make a request to the API.
The Form can not be modified when it's open in View mode. You can't make an external request to an API, and then display something in the Form to the user.