Yes, this requires a Power Delivery USB-C power supply, e.g. this one:
Ugreen GaN Fast Charger (100 W, GaN Technology, Power Delivery 3.0, Quick Charge 4.0)
The Steam Deck has a "45W USB-C-PD3.0-Netzteil". USB-C is default and the Icy Box can handle up to 100W.
So, I don't see any reason why it shouldn't work.
I don't know, if you can use all other ports with the Deck, but that should be possible, since Steam Deck describes:
"USB-C mit DisplayPort 1.4 mit Unterstützung von Alt-Modus; bis zu 8K mit 60 Hz oder 4K mit 120 Hz, USB 3.2 Gen. 2"
So the Video Outputs should work too.
I can't answer USB-C to connect your monitor to get a picture. If your Monitor has USB-C hub that works to use those USB ports as well. However you can charge a laptop but my dock gets very warm even i just have a HP 435 G8 (45W).