No. You cannot plug an Ethernet cable directly from an Xbox 360 to a PC and expect networking to work. Here's why and what to do instead.
Share PC's internet (Wi-Fi/Cellular) to Ethernet port for Xbox. Unreliable, adds latency, breaks easily on Windows updates. Buy a $15 travel router instead.
Bottom line: A router is the only robust, zero-config solution for Xbox 360 networking.