Writing a POP3 client for the Xbox is fairly trivial. However, it isn't possible for it to run in the background while playing games. No point in arguing that, it's just the way it is.
But, it wouldn't be a problem for any of the dash authors to build it in when they have time. I'm sure we'll see it sooner or later.
As for the browser, I doubt it'll happen. Even with basic HTML 3.2 compliance, it's not a weekend project. If a small team was formed for the sole purpose of writing a browser for the xbox, the project would probably take a couple of months minimum.
I'd consider getting a team together to do it, but i'm still trying to squeeze out time for jihad.