Will A Raspberry Pi Display Work With The Original Up Board?

I have a question about a display that says its made for the raspberry pi, it uses the GPIO Pins for power and hdmi for video, since the upboard is almost identical in size and board layout to the pi, would it work? i have a feeling it would but i wanted to ask just incase anyone has tried this.
also would the active cooler with a fan be compatible with this dispaly? or would the gpio pin dispaly be in the way of it and would it have enough room that little air would pass

here is a link to the display i have bought

https://www.ebay.com/itm/Raspberry-Pi-3-5-inch-HDMI-LCD-touchscreen-3-5inch-display-60-fps-1920-1080-IPS/332223007022?_trkparms=aid=111001&algo=REC.SEED&ao=1&asc=20160908105057&meid=64b52d14cbde4d429f52d343dc5f7fbc&pid=100675&rk=1&rkt=15&mehot=none&sd=332223007022&itm=332223007022&pmt=0&noa=1&pg=2380057&_trksid=p2380057.c100675.m4236&_trkparms=pageci:482c9bec-718a-11ea-8454-74dbd180f09e|parentrq:2512f5d11710aa18f1578567fffa62fa|iid:1