Is there any way to create a custom module whose fields rely entirely on a REST API?
The module doesn’t have to create a table in the database and would rely entirely on a REST call to a different platform.
Is there a way to achieve this?
This is a novel idea 
I guess you could do it by creating the simplest module (with just one field perhaps). The table would get created in the database, but you wouldn’t use it.
The you would override each view so that what happens in the view depends only on your own code (and therefore you can use only the external API).
But I never tried this, you would have to experiment.