Yes, but you’ll lose Vaio Control Center and hotkey support. Windows 8.1 includes basic drivers for almost all hardware except the Fn utilities.
Sony VAIO PCG-71811W is a product chassis code often found on the bottom sticker, but for driver purposes, it is more commonly recognized as part of the VPC-EH series (specifically models like the Laptop Hub Official Driver Status & Availability Sony has officially discontinued support Sony Vaio Pcg-71811w Drivers For Windows 7 64 Bit