Could have been. I've been trying to find out. Did Goerz make a FP shutter camera? The 5x7" Press Graflex was a pretty common camera at the time among photojournalists. Lartigue's father had some sort of 13x18 camera, which J-H used, but I gather that the family was wealthy, and he had access to various cameras.
Looks like there's a bit of doubt about that - and since most of the information on the net was written by art curators and not camera collectors, it's difficult to find out. One page stated it was an Ica Reflex. Could have been, I guess?
Anyway he had a number of cameras and used them all. At least one of them had a vertical focal plane shutter, as we see from that famous picture.
The 13x18 camera he started with was a typical tailboard "Reisekamera" (like mine), and was certainly not the camera with the focal plane shutter.