Possibly, if you have a "fat" PS2 with the hard drive bay, and then install Linux on it. You might be able to get a wireless ethernet bridge device to hook to the network adapter for the PS2. Way more trouble than it's worth though. And there's a possibility that you'd need to install some kind of exploit or modchip into the PS2, which is legally questionable at best.

So when you get down to it, the answer is effectively no.