"Do we have data suggesting this approach is in fact more accurate?"

That isn't the goal, here, although ultimately empiricism demonstrates that people concerned with explicit and conscious standards become more accurate. That's a side-effect, albeit a very nifty one.

The point is not to be correct, but to know that we're as correct as our understanding permits. If we don't understand our reasons for doing something, and we can't predict how well our choices will work out by looking at experience, we can't know whether we're doing the right thing.

If your decision systems are unconscious, but you can consciously look at their outcomes and see that they work out, going along with your feelings is rational - because you are consciously recognizing that they work and consciously choosing to follow them.

If your decision systems are unconscious, and your meta-decision systems are also unconscious, and you can't explain why you're following your feelings (beyond that you feel that you should), you're being irrational. Even if your systems and meta-systems are correct.