In-Game Browser
 

Does the current API allow or would allow an in-game browser or even some sort of sandboxed version of one?

No, and hopefully it never, ever will. That idea = attack vector for viruses.

Thank you very much for the info.

Not an addon but
 

If you have the version purchased from Steam you can use the browser in the Steam overlay.

I bought Rift a second time just for that when it was on sale.

you do not need to purchase a game through steam to use it with it's browser. You can just right click / add it to your library as a non-steam game =). That will give you access to the shift-tab when you launch it from within steam.

Also, if you want an in-game browser, you could check out Raptr. It's a chat program not unlike Trillion, except that it works in game. It includes the many different messengers so that you can stay connected to friends & family, while playing your game (or you could just not sign into any and use it as just a browser).

It supports:
Xbox Live
Playstation
Steam
XFire
AIM
MSN
ICQ
Yahoo
GTalk
Facebook

So it gives you a whole host of options, and allows you to take in-game screen shots and upload them directly from your chat client to the web and has the awesome browser function. Oh and it has a nifty feature called Game Tracking, which tracks the games you play and the amount of time played.

It's worth a shot! :)

You could try Overwolf

http://www.overwolf.com/

Lets you do tons of stuff while playing your game.