I think it is possible, but depends on how the signal is clipped. Let me explain: think about a softly clipped signal. Clipping is present only in the greatest peaks, and therefore appears for a short time lapse.
This kind of method could detect the clipped intervals and ''soften'' them, based in the previous behaviour of the signal. An statistical approach would probably work, but it is not a trivial task. Of course, you have a probability of guessing how the original signal actually was, so you will probably add some distortion. Hopefully, the result will be better than the clipped version.
On the other hand, if the signal is heavily clipped, the chance of guessing it right is unarguably lower. The signal could be anything but a peak: it has time to do lots of things until the clipping stops.
The recovered signal using the stated method would be the blue one, while in fact any signal (e.g. the green one) could have actually happened in the lapse of time we don't have info about.
Just when I thought I had come across a great idea, Wikipedia told me that I'm not the first to think about this:
Several software solutions of varying results and methods exist to counteract this problem: Sony Sound Forge, iZotope Rx2, Adobe Audition, Nero Wave Editor, and a plugin in the Audacity LADSPA package come with clip restoration software. There is also an Audacity plugin called Clip Fix that uses cubic splines to attempt to restore a continuously differentiable signal.
Please excuse the poor quality of my hand-drawn figures ;)