If anyone was lucky enough to do it, it'd be someone who isn't making money solely off music - i.e. Jay-Z/Will Smith/50 Cent.
Personally, I think Jay and Will are the most likely to reach a billion. Jay's getting caasg from various ventures (big and small): Roc Nation (360 management, publishing and record company), touring, Buffalo Burgers, NY Nets, 'Decoded' sales, endorsements, line of headphones, being featured in magazines, 40/40 club, Carol's Daughter beauty line, Greenwich Village Bistro etc, etc. And those are just the investments he's made public. He's likely to have more small investments.
Will also has the potential to be worth a billion. He's more often than not making a ton of his own movies and he even produces sometimes - where a lot potentially can be made.. His company Overbrook probably generates a lot of revenue off his and his son's movies. His daugther has hit it big with her single 'Whip My Hair', and seeing as she's listed as his employee, that's also bringing in some cake. He could easily tour around the world and make an easy 5-10 million. He's got new TV shows lined up and he'll still be getting money from the Fresh Prince. Furthermore, he's also likely to have investments that he's kept private. If he gets back to a movie every year or two, he could be a billionaire (or close) within the next 5-10 years.
Birdman (or 'Baby') will have a lot of money but most of it will be from record sales from CM/YM, thus far. He's already been exposed about his "oil investment"' claims - no one in the industry have heard of the 'Bronald' oil company. He likes to talk like he's in the 400mil+ region but he's obviously delusional. Also, like someone pointed out he's in partnership with his brother, Slim, so you need to halve pretty much everything the dude is says he's earned.
Verdict: he won't be a billionaire.