Not directly because it can't handle retransmitting the existing HDMI signal. You probably need to add a HDMI/DVI switch IC like this one: https://www.analog.com/en/products/ad8196.html
Do you know how that chip is for real-world usability?
In my personal experience, obtuse monitor's firmware is often to blame.
Using a switch with one extra input port, where all data pins are connected to ground (via series resistors), and switching to that port for a brief moment, before switching again to the real intended input, usually helps some.