PS2 online help

I know you have to have the PS2 network adapter, but if i put one in my PS2, would it allow me to play online if i plug the adapter and a Linksys wireless broadband router into it? I have a cable modem but its hooked up to the master computer in my house and i use these routers to put internet on other comps in my house and friends in the neighborhood, do you think this will work?