I would do it! If there are potential issues, they will document them and that can help you argue for warranty coverage if any issues would appear later.
Yes! Actually, that is a good idea. At least you maximize the use of your warranty before getting a new one. Like what @Evholic_18 said, there'll be documentation.
It's definitely worth getting your car inspected before the warranty expires. It's like a final checkup and dealers are good at finding hidden problems. You can get repairs done for free while still under warranty saving you money later. It's similar to a last-minute doctor's checkup before your insurance ends.