No, the PS2 controller cannot be read directly using the HID (Human Interface Device) protocol. HID is primarily designed for devices such as keyboard, mouse and joysticks that have a standardized input format.
However, you can use a PS2 emulator such as PCSX2 to emulate a PS2 console on your PC. This emulator can read input from a PS2 controller connected to your PC via a USB adapter. While the controller itself is not directly using HID, the emulator effectively translates its input into a format that the PC can understand.