Will a genuine Arduino board have the same issues with High Sierra as other non genuine ones?
As long as the firmware on the ATMega16U2 chip is the same as on a Genuine Arduino and the bootloader on the ATMega2560 chip is the same as on a Genuine Arduino then your boards should function exactly the same as a Genuine Arduino.

If you find a Genuine Arduino works but your boards don't then there must be a difference, and that can really only be in the software on the chips - so reprogramming the chips to match a Genuine Arduino would probably help.

I haven't heard reports of High Sierra not working with Genuine Arduino boards, but given the severity of some of the bugs that have crept in recently, it seems likely that more problems are hidden away under the hood that no one really knows about yet.