In general servrless (should be called lamda functions) are short running functions that glue other cloud provider functionality/services and generate/react on cloud events. So would say this architecture does not match Phoenix functionality as Phoenix was designed as long running process.
But I suppose you could write some lamda function in Elixir.
Preferred languages are with quick startup times like javascript, go …
AWS lamda limitation
We have some forum thread about server less.
