As I mentioned in my message - make them available from the system tray
Yes, but icons in the Systray are not 'Desktop Icons'. The systray and Start Menu are levels above the desktop and are set to be visible above open windows when in focus. That's the level that Docks work at as well.
Fences is designed to manage the Desktop Icons at their level. It cannot relocate the Desktop Icons from anywhere other than the desktop.
Think of it as like the Start10 program. That works at the start menu level and doesn't change its level.
Both programs are designed to not impact on 'expected' functionality. When levels are messed around with there will always be action conflicts...often seen as 'click through' ...where you want to activate one thing...but end up inadvertently activating something below [behind] that you didn't see.
All of that is not to say that a program could mimic or copy the desktop icons to another level [they would no longer be desktop icons] and be accessible at another level...exactly as Docks do [which is why they exist]...