No, it doesn't.

Say I pass the invert a tree question. Does that prove I am good? That I can design a product, listen to customer requirements, come up with ideas that elude others, read a research paper and turn it into something commercial, solder a circuit board, make a schedule, mentor junior engineers, write documentation? No. All inverting a tree tells them is I studied trees recently, and/or I'm at least superficially clever.

Google lets go of plenty of people. They aren't making perfect hires.