It doesn't work and pretty much makes the artifact go from pretty good, to very lackluster. So the problem is that a shotgun kill will never trigger the second melee. So if you get a shotgun kill, you get the overshield for that one. If that runs out and you get another shotgun kill it doesn't trigger the second melee and give you the shield. Your regular melee consumes it and the shotgun will consume the first charge, it just wont trigger the second charge,. You need to wait the 25 seconds. No Backup Plans needs two fully charged melees before you can trigger the exotic perk.
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Void fang vestments and lucky raspberry don't proc with full grenade energy either. Only get 1