Most likely not just any arbitrary APK

https://gitlab.steamos.cloud/frame-public/lepton

Lepton is intended to help game developers bring their VR Android games to the Steam Frame. Other usecases are possible, but were not the focus of development and may lack polish.

From what I understand, if you try to launch a flat application, it attempts to launch it in VR mode which is screwy. It best, not a useable experience.

But maybe some day. This certainly lays the groundwork to allow that functionality eventually.