I dunno. It seems like I can injure myself without trying. Maybe I'm defective. I have had what I considered good workouts only to wake up the next morning with a pinched nerve in my back or another joint problem. Muscle soreness feels good in comparison.
Yes you can push harder. That extra burst of speed from our evolutionary past doesn't care about strains, sprains or breaks. Because if you don't get away from the big bad wolf you won't have any injuries to enjoy.