It doesn't seem to work. It gets picked up as "Billboard device" but doesn't output any signal to the display.
I tried the obvious: checked the display, the cable, tried the adapter with different devices (Thinkpad E480 and OnePlus 7Pro, with both it worked just fine).
In Dell's specs for XPS 13 9370 it states that "A USB Type-C to DisplayPort adapter (sold separately) is required to connect a DisplayPort device." which I discovered just now. Does that mean that I just need DisplayPort adapter? Or is there a way to make the HDMI one work?