Serverless is not caring about your servers, not only Function as a Service, if you use Now or Heroku you're using serverless, you don't need to care about the server and how it works, that's the idea.
And yes, you can use serverless to build your whole API, even the frontend, you could create an API and deploy it to Now as a single app or tiny microservices or you can create a lot of tiny functions and deploy them to AWS Lambda and compose them to create a proper API.
So it's totally possible to run your application in a serverless environment.
We're a place where coders share, stay up-to-date and grow their careers.
We strive for transparency and don't collect excess data.