Corrections and retractions. Maybe a better analogy would be the spontaneous formation of cyclohexane from ethylene. Also the Pauson-Khand does not go through a pericyclic mechanism. But either way, you've got the two tethered alkene "arms" which are sill relatively free to move about, and a second alkene equivalent which is also free. Can't say it won't happen, but this reaction would be very entropically disfavorable.