Yes, tenacity is basically useless in "purge the alien" missions.
I actually just posted a thread on this last night.
The objectives you're referencing, specifically slay the warlord, only matter if the warlord is dead. He is not, himself, an objective. His death is. So, if you can draw 3" from a dead model then sure...but unfortunately you can not. :( Trust me, I was excited to have tenacity on my crons only to get purge the alien as the mission type. *Sigh*
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