It seems like an absurd strategy to me, to deliberately add random noise to your decision making process, and then try to filter that noise with an average. Maybe if the random priming approximates gathering evidence closely enough to compensate for the incompletely filtered noise, it could work. But if priming just causes you to irrationally add more weight to evidence you already considered, it is not helpful.

On the other hand, if random priming leads you to have an insight that you could analyze, that could help. Even then, you should wonder why your other strategies to achieve insights are Worse Than Random.