no, no drilling.
just to be clear.
horizontal mounting -> just clip it on to the stand ie the same procedure as the original stand.
vertical mounting -> you need to first screw on the included 100mm vesa plate to the monitor, In the orientation you require. Than mount the monitor on as required
hope that helps.
ps if you only use the plate in vertical orientation, the two monitors will not be flush, I have mine slightly in a V shape, but if you want both monitor bezel to be mounted flush you need to mount both monitors using the vesa plate.
hope that helps