Average is irrelevant in being able to tell a difference in drillings. For that matter, you don't even have to be a bowler, period. You can watch someone else and as long as you know how accurate they are (say, when watching a pro bowl) you can see the difference in their ball downlane.
Anyone with some mental ability regarding layouts want to tell me you can't watch Chris Barnes throw a pin-down, 2-inch pin-to-PAP ball and notice the difference when he switches to a pin-up, 6-inch pin-to-PAP ball? I would hope you can. Surely in person, but even on television.
As to one's own game, yes, I believe anyone with even a modicum of skill would notice the difference in reaction shapes if they took the time to learn about it. That's a learned skill that is separate from bowling ability -- and it's one that not every bowler, even some very successful bowlers, ever learn or care to learn. I know 170-average bowlers who know far more about their arsenals than some 230 guys.
What average is, without dragging the oil pattern into it, is a measurement of two things: (1) Your physical bowling ability, and (2) how well you can apply what you know mentally to the sport.
I average right around 190 and can definitely tell the difference in layouts. The reason I average 190 is because I can't repeat the shot well enough and my house doesn't lay out a fluff shot that covers everything up. When I miss, I tend to pay for it, and my knowledge of surface/layout/etc. lets me know exactly how I'm going to end up paying for it before the ball gets halfway down the lane.
Jess