Can I use the SHUNT to self-belay?

No, the SHUNT is not authorized for self-belaying, for many reasons, including but not limited to, the risk of the cam jamming in an overhang situation.
For more information on self-belaying, go to: https://www.petzl.com/US/en/Sport/General-principles-for-solo-climbing-with-a-fixed-belay-rope?ActivityName=Rock-climbing