No, you don't just need the 360 wireless adapter. There are other wireless adapters you can use. Right now I use the Logitech Playlink for my PS2 and 360 but I'm going to get a 360 wireless network adapter because switching the ethernet cord between the two systems wore out the clip at the end. You can get a Logitech Playlink real cheap now. I've never had a problem with mine. Before you hook the one you have for your PS2 up to your 360 make sure it says the product is compatible with the 360.
logitech playlink - Froogle
*EDIT
If you do want to get the 360 network adapter go to froogle as well. There are a few on Ebay that are going for $69.99 + $9.95 S&H. That pisses me off because I had just ordered it acouple of days ago fom ebay and the cheapest one they had was $10 more. Anyway, you can get it for about $20 cheaper than you would find at the store. Link =>
eBay: Microsoft Xbox 360 Wireless Network Adapter (item 180056666121 end time Dec-27-06 08:48:12 PST)