You're being too cheap though. Cheap to the point of "hell no, that doesn't work."
The official hard drives for the PS2 have some odd proprietary firmware on them that the PS2 specifically looks for. Also you'd need the HDD Utility Disk to setup the drive and Sony doesn't hand those out. Simply put, if you want a PS2 hard drive, you have to buy a PS2 hard drive. That being said, you can find them for about $89 at most places.