By applying the pre-exhaust method, you've practically changed the whole balance of which muscle becomes the primary activator /dominator; which muscle becomes the secondary and less dominant, and most importantly, you've altered and shifted the whole equation of the time factor. So to answer your query directly, I'd say the posterior chain would just be about waking up, when your quads have had it. So no, there won't be enough time (enough reps performed) to fully engage and tire out your posterior chain before your quads have been fried.
Olympic weightlifting shoes would not allow for more quad activation in and of themselves. If anything, what you get in a direct manner through the wearing of this shoes would be more knee stress (and in particular the partial tendon part of your knee). No I'm not putting weightlifting shoes down in the least, I've been wearing then for over 30 years. I'm simply giving you the facts I see on the ground when one lifts their heels up could of inches off the ground. As far as quad activation goes: the shoes would help you in keeping an upright stance (your torso that is) than if you didn't have them on and had a terribly tight ankle / lack of ankle flexibility...., which by the way you (and everyone else) squatting would benefit from stretching them on a daily basis.
Weight on the bar is only relative 9up to a point), and should never be your standard of what is really taking place at the cellular level deep within your muscle fibers. In a nutshell, forget weight and focus on effort. Effort is the only language your muscles and nervous system understands and responds to. Weight on the bar might attract the girls though, feed your ego, and possibly lead you to an injury you'd have been rather better without. Just saying