I have seen several videos about the Razer Core v2 and other EGPU manufacturers. That works as far as I know, but you lose performance if you run the EGPU via the internal monitor. You generally have a performance loss because your graphics card is only connected via 4 lanes instead of 16. (However, you have to install Windows via Bootcamp if macOS High Sierra does not yet support all of this).

This has less to do with the hardware and more to do with the software.
As a rule, yes, it can run via the internal screen.

Otherwise, I can recommend this website, everything is described in detail there.

https://egpu.io/