I know it's possible with ArcGIS for Server (which has a "ArcGIS Data Interoperability for Server" module etc.) - I'd just have to move the data to Server and all would be good.
However, are there other options? e.g. perhaps there is a tool that can export data (as GeoJSON - which Leaflet likes) from ArcGIS Desktop.
I'm considering doing an ArcGIS Desktop add-in (extension) to export to GeoJSON if there's nothing out there.