Blizz just simply won't allow those possibilities at all. As Lykofos stated, there is nothing for them to gain out of making such a transition and "opening" their sandbox like that.
I'll give you a good example why this could be a bad idea. I currently use Skype to keep in contact with family since I've moved. They know I play WoW and using Skype is the only way to get in touch with me. However, while having to keep this program open, I'm liable to get spams from others wanting me to add them to my friends list. I have to report and block these spammers at least 10 a week. And this goes on for a good period of three or more months.
Now imagine Gold Spammers doing this to you while you are playing game using chat programs like this and Blizz allowing your to have this capability initialized in their game. The outcome would be near catastrophic and would actually ruin the game for quite a few folks.
While the idea is good, and the intentions may be sound, the execution could very well ruin the entire process because there are people out there who have nothing but the worst intentions for folks with good ones.
There are other ways though to solve this simple issue that you are having. They may not be what you want to hear, but they do work and that is alt+tab or run the game in windowed mode. They are safe, hassle free, and it doesn't cost anyone any extra money and development to open up a potentially dangerous can of worms.
As far as I know, the new Battle.net system will have some pretty spiffy additions that will also make people who don't play WoW possible to get in touch with you. I'd suggest l
Battle.Net to see what they have to offer for what you would like to do. Also
this should help you with even more detailed information about the new Battle.Net system.
Trust me, we're not knocking you for your idea or suggestion. It's just that a lot of us have seen what outside programs can do to ruin good games and communities. So we're offering suggestions to help you enjoy the game and your friends without the potential hassle.