This was something I definitely didn't think about, but it is possible! In the Steam Deck Client Beta update from October 20th, Valve added the ability to add in your own virtual menu icons! These icons are in the form of .png and you can get to them in this folder:
~/.steam/steam/tenfoot/resource/images/library/controller/binding_icons
By doing this, you can download, drag, and drop your pngs here and they will appear in the "user" tab in the virtual menu.
Today, we were shown a reddit post by user wearedefined that shows an animated image in a virtual menu.
I thought this was interesting and realized that animated png files exist! So I decided to test this out. I dragged and dropped an animated png I found (the first one I found) and renamed it in the binding_icons folder. I opened up my Deck and there it was, in the user tab, dancing. I set it up and went in game and, lo and behold...
This is pretty insane to think about, but now we can have animated virtual menu icons for our games! You still have to manually add them, and you gotta either make or find the png, but...it is possible!