Can you register a user to an application at the same time as you create them

Would it make sense to provide a User + Registration API creation that also effectively logs in the user and returns the access_token?

Is this what you are looking for?: https://fusionauth.io/docs/v1/tech/apis/registrations#create-a-user-and-registration-combined

That API does return a token as of v1.17.0.