Well, not likely but the threat was made recently in court by the RIAA. Their brief basically said that if you copy a legally purchased CD to your computer, it is illegal. Would they threaten to make a case out of it in court? Perhaps not now, but as the record industry becomes ever more desparate, it could very likely happen. This is what happens when the record companies cling to a business model that died years ago. They are so desparate for revenue that they want you to buy a new copy for every device you want to play it on. According to their logic, if you buy a CD, you can play it on a CD player. Want to hear the songs on your computer? Either play the CD in your computer or buy and download new tracks for your computer. This argument appears to go against what some major labels are doing now: releasing DRM-free MP3 tracks. Would the RIAA argue that if you burned a legally purchased MP3 track to a CD, it would be stealing?
In talking with my musician friends, there are those that still cling to the model of selling recorded music, either through downloads or crusty old CDs. Then there are those that are thinking ahead and giving away their recorded music and making money through touring and merchandise sales. The pay-what-you-want model, recently used by Radiohead, is another interesting experiment.
To me, the music industry is dead and good riddance. Thanks to the Internet and low-cost recording technology, nearly any artist can make a career for herself if she's willing to put in the time, effort, and money to market herself, record good songs, tour relentlessly and build a solid fanbase. An artist simply doesn't need a record label anymore.