Sounds cool in theory, but my small experience with a past company's serverless API is that it made impossible to debug. It was like deploying to a black box. There's no way to hit the API locally, etc.
https://www.npmjs.com/package/serverless-offline
I have no idea if this exists for other languages but its what lets me develop and test my functions locally before deploying them to stage/live.
Edit: they have some good examples - https://github.com/serverless/examples/tree/master/aws-node-...
pretty sure similar tools exist for some of the other supported languages.