well it would be better then nothing. I know that some games are broadband only, so you might want to look into that. Also, a lot of people quit online games when it is to laggy, so you might not want to.
I doubt that your ISP will charge more for online gamming, all you have to do is just plugin your "Ethernet" cord into your PS2 and set it up. That's what I did and I was online in moments. I been playing online games on my PS2 since it first released the network adapter.