A quarterback with pocket awareness or elusiveness will absolutely make his OL look better. The subtle shifts, moves, steps, to "safer" positioning allows a slightly bigger margin for error.
I have always supported Tannehill... and he has improved every year for 5 straight years... but he has SUCH poor footwork in the pocket and has such a lack of elusiveness that it simply leaves no room for error for the guys protecting him.
He is the essential "do your job" guy - if Tannehill was an OL player he would be a solid guard... if he was a WR, he'd be excellent at running slants, and posts, and Hartline-esque route tree... if he was a RB, he'd be an excellent Eddie George 3ypc hit the hole straight each time...
Tannehill tries hard, he has excellent skills, but he doesn't have the "it" factor that a QB needs... he needs a Ravens/Buccaneers/Seahawks all-time type defense around him to be put out a Brad Johnson/Trent Dilfer type season... he's good enough to win - when EVERYTHING ELSE is perfect.
His lack of in the pocket footwork/elusiveness/awareness is ultimately what brings him down, where you can see he is soooo much better than Osweiler but works the pocket SO much worse that the results are "toss up".