Sometimes!

Modern AIs have very limited metaknowledge - they don't know exactly where the limits of their capabilities lie. So you can get things like "a task is doable for an AI, but the AI thinks it's impossible, so it doesn't try hard enough".

Usually you get the opposite - AI overconfidently trying at tasks it has no conceivable way of reliably solving, falling far short, and failing to self-check, fail gracefully and self-report the task as failed. But having piss poor metaknowledge cuts both ways!

So you can, in fact, get better performance sometimes by applying some variant of "assume this problem is solvable" or "other problems like this were already solved by AIs" pep talk. Not always, far from it, but it does happen on the occasion with frontier capabilities.