This is very much gamescope / window management territory rather than DXVK territory and many games already do this anyway or stop rendering entirely.
TLDR yes, possible, but I really don't want to implement this since fucking around with window messages is guaranteed to give everyone a worse time as evidenced by past experiences with D3D9. There's other projects better suited to do that.
Nothing extracted yet.
Would it be possible add an option to detect if a game is in the background and if so, cap its framerate to a specific value?