If they were to put a browser it should: 1) Have keyboard support (mouse doesn't matter. The analog stick can be the mouse) and 2) Make it accessible from mid-game. It would be cool to go online and order a pizza from papajohns.com while playing MGS4 or something.
If they do put a web browser, I'm very sure that it will have keyboard support that you can connect to a USB slot. Now about mid-game access, I'm not too sure about that but I hope they have it. Still, it would be cool without it, but not as cool.