Can a Purchased MacBook Pro undergo a processor and memory upgrade?

Sorry, it isn't possible to upgrade anything in the current MacBook Pro after purchase.

No.

The processor, the memory, and now the chips representing the boot SSD drive are all soldered down for improved reliability.

Did you look at Apple refurbished? Apple refurbished are not beaten up -- they are systems that for reasons of commercial practices are no longer legally eligible to be sold as new. Apple refurbished direct from Apple are eligible for apple warranty and applecare, and are in Pristine, like-new condition.

https://www.apple.com/shop/refurbished/mac

Do not dwell on processor speed unless you need to run Compressor. Todays Macs have enough processor power to do just about anything, and a faster processor buys you nothing additional -- other things like RAM size and boot drive determine the system speed, not processor speed.