Do conical intersections really matter?

Conical intersections [where the potential energy surfaces of two electronic states touch] are ubiquitous in photochemistry. Their most important role is that they can explain why some photochemical reactions proceed so fast (i.e, on the scale of 10's of femtoseconds). However, an important outstanding question is:

Does the Berry's phase [geometric phase] associated with the conical intersection [CI] have important observable consequences?

There is a nice 2005 Perspective in Science by David Clary which discusses this for the specific case of the simplest possible chemical reaction  H2 + H to H + H2. It seems that [contrary to what was claimed in the 90's] molecular scattering experiments associated with the ground state surface below are not sensitive to the geometric phase due to cancellations of terms associated with different angular momentum channels. However, showing this cancellation is rather subtle!

Aside 1 : the CI here arises due to the degeneracy of the E irreducible representation associated with the C_3 symmetry of the transition state which occurs when the three H atoms form an equilateral triangle.

Aside 2: For more background see the nice Physics Today article by Berry, Anticipations of the Geometric Phase.

I thank Seth Olsen and Ben Powell for discussions stimulating this post.