Fear of death, desire to continue living, interest in the inner workings of living systems, helping people overcome physical trauma and illness...all of these and more probably drive our desire to prolong the life of the body. While we seem to be successful at increasing the average lifespan, we have yet to make much progress at increasing the maximum observed lifespan of the body - not to say that we can't.
I can think of two ways that the PMR rule-set can impose the mortality of the body; physical limitations (entropy increase, contamination, and general system breakdowns) and consciousness inhabitance. The first is pretty easy conceptually - the body becomes less reliable, more prone to outside influences, and more likely to mutate. The second has to do with the relationship between consciousness and the physical body - the mechanisms by which consciousness inhabits a body, what determines suitability for consciousness habitation, and where the causality for the application of the mechanisms resides.
"and if it were to succeed, what the effect on the evolution of a) our species and b) human consciousness in general, would be?"
If possible, it would slow evolution. For our species, the rate of change would decrease, thus slowing evolution - for consciousness, we would never get to flush environmental variables. The beliefs and concepts of an individual would continue indefinitely and evolution would become asymptotic (approach zero) as the system's resistance to change increased (as a product of belief traps and limiting concepts). I think the evolutionary imperative is applicable here.
My hypothesis is that inertia keeps consciousness from overstaying it's welcome through the requirements that the PMR rule-set places on the habitation of a body with consciousness; that once one of the requirements are no longer met, the body is no longer suitable for consciousness. I think an interesting thing to consider is whether or not the body can continue to function normally without consciousness. And this begs the question - Are zombies evil? ;-)