How to get started webmapping with xyz-tiles and Geoserver?

I´m starting to explore the possibilities of web based map presentation. Therefor I have a basic question in understanding. After reading a bunch of tutorials, could a workflow work like this?

1. Style a map (osm-bright) with tilemill


2. export styled map in mbtiles format


3. convert mbtiles format with mbutil to xyz-tiles


4. use geoserver to create a wms with these generated tiles (is geoserver able to serve tiles or do I need another component like a tile server?)


5. create a viewer with openlayers which shows my styled map tiles