Recently, I accidentally cracked my new MacBook Pro screen. There are rainbow lines going across the screen in different directions. I sent it into my school's IT place and they were going to send it into apple with an estimated cost of $800 since it was a tier 4 accidental damage. However, a while ago, the corner was dented from dropping it (I had a case but the case did nothing). Will apple fix that while they are fixing the screen? Or will my screen not be covered because my MacBook has a dent in it? Will it cost anything extra?
Any and all accidental damage (including that dent you're worried about) will be fixed when sent out to depot at tier 4 pricing. The glass, LCD, and housing will all be replaced- basically the whole top of the computer.
The only way it wouldn't get fixed is if the repair facility tech determines your computer "beyond economical repair" and that only happens if either a)every part in it is damaged or b) it contains some kind of biohazard (like insects, or bodily fluids) If that happens they just send the computer back not repaired at no cost. Basically on a 13" computer 755+tax is the most you can pay so they should fix anything/everything that is wrong/damaged and if they don't you should complain/send it back.
Honestly if you're close at all to an Apple store, display repairs are often significantly cheaper than flat rate tier 4 repair. When I left Apple in 2016 MacBook Air displays were around 425$ or so after labor, and 13" MacBook Pro screens only a little more than that. Way cheaper than 755 if nothing else is wrong w/ your computer. An in-store repair would also include repairing the glass and dented housing because in-store technicians don't replace just the LCD, they replace the whole display assembly.
Source: worked at the Genius Bar for 4+ years