Usually you plug the eGPU into a monitor directly instead of backfeed it to the built in display. The bandwidth is already low enough without showing rendered frames back across the link too.

There are some limitations on the PCIe/Thunderbolt but Marcan has written a few times he thinks it may be possible though probably not worthwhile from a performance perspective. Of course even base thunderbolt is a WIP at this point so that answer could always change.