Can we rationally act in an irrational manner? I reason so.
First let us understand what it means to act in an irrational manner. I would argue that feeling happy for no reason constitutes irrationality, almost by definition as if we have no reason for doing something then we have removed reason and thus it doesn't seem rational.
Yet if I have an irrational belief that generates vast amounts of happiness for me, would I not rationally harvest the bounty of such irrationality? I can think of few things more rational than getting a free lunch.
Of course, we have to pick our irrational beliefs very carefully in order to actually derive a free lunch. If we believe "god will provide all that I need" this could provide us with a profound degree of security and comfort, yet it could also prevent us from taking the action necessary to secure our own needs.
Three years ago I decided upon one central belief. A belief that many skeptical scientific materialists would call pure superstition and dogma. I chose to believe in my own free will. I found this belief one that reinforced itself the more I exercised it.
On some level a belief means something we lie to ourselves "enuff" until it be.
Do I have any solid rational basis on which to know I have free will? Many would argue I don't. Yet does this belief bring me great satisfaction in life? It does. So rationally I choose to continue this great experiment in human freedom.
Other beliefs I have adopted that flow that first belief: I can change the state of my own mind through will alone, I can feel happy for no reason.