former mechanic here: i always test-drove every vehicle before and after an alignment. sometimes the pre-drive revealed problems that had nothing to do with the alignment, or that it didn't really need one after all. sometimes it's as simple as a low tire (plug the nail-hole), a radial pull from a defective tire, or even a completely unrelated problem that the customer self-diagnosed incorrectly. quite often people would say it needed an alignment even though it drove arrow-straight, and it turned out that they thought the steering wheel shaking (whether only at highway speed (wheel balance) or only while braking (warped rotors)) meant it needed an alignment. i've also had to explain to people that most cars and even many trucks/suvs need more than just a FRONT-end alignment - with independent rear suspension, you need to adjust the rear as well - and do it before adjusting the front wheels, because changing the rear changes the thrust angle.
another good reason for a post-alignment test drive is in case the alignment machine was faulty, accidentally selected wrong year/model in the computer (which means wrong specs), or if you perhaps didn't install/calibrate the wheel sensors properly, or they came loose during the alignment, or even because of a bent vehicle wheel that isn't obvious when it's not spinning. it's rare, but i have had to re-do alignments because of those reasons, and i'd much rather re-do it BEFORE i give the vehicle back to the customer.
the only time i ever pushed a customer's car hard is if they specifically said that the problem happened under hard acceleration/braking/steering/whatever. my favorite was when the dealership's owner hit something in his 911 carerra 4s, he came to me specifically because he knew i raced and was an instructor to boot. thankfully i was able to find the problem, and it actually did need to be pushed close to the limits to find it - under normal driving it was fine. that wasn't easy to do on public roads, but me being me, i knew a few places i could get away with it.
turned out the front strut and control arm had very minor bends (had to measure the control arms and compare to find the difference - there was no obvious damage to the arm), and in hard left turns, it was just enough to make some weird noises that didn't show up in hard right turns.
