Should is one thing, would is another.In fact, Chord recommends a 5V-2A power source to utilize the desktop mode on Hugo2, so I think that the Thunderbolt 4 is able to manipulate it.
Hugo2 does not use the power of USB input for power.
It has TWO usb sockets, one is exclusively for audio input, and the second is exclusively for power input.
How you are going to swing that, I wouldn't know.