No,its only if you then make it available for others publicly.
Do libraries pay royalties to authors?
Not sure,but in some circumstances radio stations and clubs pay for public broadcast rights.
Now. If I were to buy a loaf of Wonder bread, find out their exact recipe, start baking my own loaves and distribute them free (not for profit) to my friends and family -- if millions of people had access to that recipe and shared it with others -- would the Wonder Corporation have a snowball's chance in hell trying to sue thousands and thousands of people for "infringement" of a patented recipe in court? Remember, there's no profit, just sharing. Think about that for a second.
As for the RIAA, they are victims of their own lethargy. For the same reason companies like United Airlines and Xerox file for bankruptcy and become shadows of their former influence and market dominance, the RIAA finally figured out that rickety noise in back wasn't a bump in the road, but the entire wagon getting unhitched and left in the dust.
At the rate they are going, certain artists can become (and some are) corporations unto themselves. The Madonnas and Celine Dion's of the world can finance their own music and publicity and will always have products that people will buy in the store (for pleasure, for gifts, etc.) Others, for example, The White Stripes, have grown in immense popularity by word of mouth. Someone downloaded such-and-such by the White Stripes from Kazaa and brought it into work and played it on the computer and everyone heard it and loved it, blah blah blah -- instant sales. Self promotion with little or no effort except having written and performed the music and technological Fate made for COST FREE publicity across the globe.
But if it's on your hard drive, you're going to jail.
The thing that makes America awesome is that we are never allowed to rest on our laurels -- in any facet of life. RIAA fell asleep at the wheel. Someone stepped into the gap and developed the kind of computer technology that would bring near-professional level recording capabilities to your den (at the cost of buying a computer).
The next play belongs to the RIAA. They'd better think twice before making a move that will leave them with a real checkmate.