We can all conceive of hypotheticals like this. And it certainly is possible. The data just tends not to support it, though. We've looked in quite a few different places, and we just can't detect any effect like this. That doesn't mean an effect doesn't exist at all. But I think it does mean it is at best small.
I think there are a few reasons for this
(1) When there is a lot on the line and we take a long time for each shot and care a lot about the shot's outcome and study the potential patterns for a while, etc, that feels very different from a more casual several-second study of the table followed by a brief muscle-memory execution of our normal shot routine. I'm not convinced the outcome is very different, though.
When you are at that place where you can go for the bank shot or play safe and it is a close call, you imagine you might play safe it it "mattered" and go for the bank shot in league. This seems like a big difference. But it's like whether you hit on 16 playing blackjack. The big picture is it really doesn't matter that much. If you're feeling it is a close call, it probably is. And the outcome is pretty close to the same if you're playing loose and a little aggressive or playing more deliberately.
(2) Chances are if a league or tournament feels casual to you, it probably does for others as well. So while YOU may have a few drinks and not warm up and not have the speed of the table down before your game, that is likely. true for your pool of opponents as well.
Even if league is dead serious to you and others are playing loose, it probably won't matter.