Having spent day after day behind the Genius Bar doing little more than fixing broken iPhone screens (and/or swapping out dangerously frayed lightning cables for iOS devices still under warranty), I can emphatically answer "YES". Most of the time we could tell because the screen actually felt different to the touch or looked thinner. Sometimes we would check the device in only to notice certain tell-tale signs once we got it back to the Genius Room (yes, we actually called it that) where repairs actually performed. If we caught it at the bar, we'd hand the phone back and say that we couldn't actually work on the device. If we noticed it when it was in the back, we'd have to make a note of it in the work order, and the not-so-lucky Genius who was scheduled to return repaired devices to customers that shift would have to have that talk with the customer (oftentimes with a manager nearby in case the customer started getting mad).
At this point, there is so much glue on the inside of most electronics that almost anyone can pretty much tell when they open it up, because it's no longer fully sealed. It's been a while since I worked for Apple, but $130-ish (or whatever the screen replacement cost is now) isn't so much more than a "sketchy repair shop/kiosk" to deal with voiding your warranty. Plus, a lot of those places won't be able to calibrate the screen correctly -- resulting in other issues like your TouchID sensor no long working.