if you shoot a drop away rest does the stiffness of the arrow matter.

yep

Drop a ways are a bit more forgiving, but spine is still important. However any properly set up rest and a release aid with a string loop will shoot well with a stiff arrow vrs a weak arrow.

Drop a way rests are not magic, I don't care what you read. They are a rest just like any other and basically do the same thing. The only advantage they have is they move out of the way to allow for better fletching clearance.

Paul