Awareness makes a difference in my games.
I really see it in pocket presence and seems to impact how/when some of the traits are applied (like if the QB has "Throws Ball Away: Yes" and "Force Passes: Aggressive" seems to dictate which of these takes place and when) - also seems to impact defender performance against the QB. I have an easier time getting picks (I don't switch, so it's CPU doing it) against lower AWR QBs than high AWR QBs, even if the both threw it right to a defender.
CPU QBs with higher AWR tend to at least attempt to buy time and get the ball out before the sack, if not just take off and run. Low AWR QBs tend to just stand there and get pummeled.
And if a QB throws a pick once every 7 passes, that's....pretty damn bad (14%!). The average INT rate was 2.6% last season. The WORST rate was 4.2%.
If the 6 passes were to largely open WR, AWR may not have mattered as much, but if he tried to fit the ball in to tighter coverage, AWR may matter then.