Hi GB18.
I don’t know for sure, but I would expect your setup to work OK.
I have a desktop with 2 monitors using the HDMI and VGA ports, and have successfully had my chromebook work as a 3rd monitor through wifi. The chromebook appears on the Windows > System > Display as monitor 3, and extends the display.
I even had a tablet working as a 4th display at the same time!
My only issue was that I found that the chromebook and tablet were a bit laggy.
Attached is a screenshot showing (left to right) monitors 2 and 1 followed by the chromebook as monitor 3.