The reason I bring up the question is there has been some interesting tweets by Jeremy Crawford that seems to possibly open the door for this interaction.
Jeremy Crawford (Lead D&D Rules Designer) stated this via twitter:
The Hex Warrior feature is intentionally worded to extend its benefit to two potential weapons: the weapon you touch and a pact weapon you conjure.
More Jeremy Crawford:
When we wrote "every pact weapon" in Hex Warrior, we really meant every pact weapon. #DnD
As a reminder The Pact of the Blade feature states thus:
You can use your action to create a pact weapon in your empty hand.
So, my question is can the Shadow Blade weapon you conjure be used as your pact weapon and thus benefit from Hex Warrior (or is the Shadow Blade spell dead weight for a Hexblade)?