Can you mirror an iPad to a TV via HDMI adapter while iPad is locked?

I have an iPad connected to an HDTV using the [Apple Lightning Digital AV Adapter] (http://ift.tt/VFGj14). When the iPad is on everything works nominally: the iPad screen is mirrored to the TV.

Is there a way to continue to push the screen contents when the iPad is locked or smart cover closed? I don't need to see what's on the iPad, I'm basically just using it as a projector.

I know airplay will continue video playback when a cover is closed (at least in some apps). I'm trying to do the same thing over the Digital AV Adapter cable.