Yes, you can use other sources for vector tiles. This fiddle has an example using tiles served by tegola. You just need to be more explicit with the sources of your vector tiles in your
style.json like so:
There is one caveat, however. While the mapbox tile spec allows for vector tiles from multiple sources to be used in the same layer (e.g. tiles from Mapbox AND ESRI in the same layer), the ESRI JS has some quirks in it that do not allow that to work. I've written up info on tha bug here.