No, but the number of unwinnable hands is quite small. Visit the FreeCell FAQs from Staffan Nählinders and Michael Keller for answers to this and other questions regarding the popular solitaire included with Windows 95.
Also, check out Thomas Warfield's FreeCell Plus and FreeCell Wizard, and Zonora Technologies FreeCell Collection, for even better implementations of FreeCell, along with a number of variations and related games.
