More awareness would mean a quicker chance of break run block, but he may not break off. You typically need some kind of angle for BRB to allow you some slide. And there is a blocking interaction every .7 seconds or something. So if you win the pulse, you will just try to win again and again. I wouldn't worry too much about trying to initiate a run blocking interaction sooner than a pass blocking interaction, it's such a small issue in my opinion, and blitz aware is cheap, your guy will be fine. There is also a small radius, or halo, range around your player that auto triggers pursuit mode, without waiting for a blitz aware check delay (the end of pass rush mode) once a ball carrier enters it. So as a ball carrier heads for a rush lane, your linemen will attempt to break run blocking.
On pitches, you can't stop pass rushing until the QB releases the ball. Then, and only then, will your players roll a blitz aware check to see how fast they begin pursuit mode. Typically a blitzing linebacker or DE, as you know, are already past the running back when this check happens. So pitches are effectively kind of mini-screen passes which is weird. You just have to hope the DE can sack the QB before he gets the pitch off at that point. This occurs occasionally.