my n of 1.
i ripped my plantar fascia about a decade ago. then my post-tib in the ankle, cycling. then had a calf pull. then the rear side of my heel. then the outside of my knee. all on the same leg. nothing ever felt bad. it was all very very low-level and indiscernible when running. there was never any pain prior to an injury. but the injuries accumulated., due to scar tissue.
if i had done one downward dog, anywhere along the way, i would have felt the way the scar tissue in my first injury was going to influence the kinetic chain all the way through my foot to my ankle to my calf to my hamstrings to my hips and up.
in my opinion, yoga asana (stretches), and work to resolve the scar tissue, would have benefited me greatly. both from the flexibility -- with no need to go overboard -- and the body knowledge it would give. so, stretching = flexibility & body knowledge.
regarding the religious side of yoga. every religion has its esoteric vein -- qua, i would say, foundation. the christian esoteric / mystic tradition is largely unknown and, as this post illustrates, actively denied / negated. very interesting. as isaiah berlin said, "no straight thing was ever wrought from the crooked timber of humanity." today's mainstream and evangelical christians might/do? find trouble with yoga's spiritual intent. but would jesus? what was he doing in the desert for his 40 days? // the intent of yoga asana in the eight-fold path is to prepare the body for meditation, and the point of meditation in this case is spiritual.
but it stretches the body a bit for running, too.