if it is a 1080p screen yes

No, because it is HDMI 2.0b, Max. 4K resolution as well as Max. 60Hz, if you want to achieve 120Hz with HDMI, you would have to look for version 2.1.

2.1 can do 4K120Hz as well as 8K/60Hz.

If you really want the 165Hz, you would have to go for DisplayPort.