Technically there is no requirement in LEED to stop you from registering and certifying a project that has already begun construction. But it can be tough, as Jean notes.
Another obstacle is the fact that LEED really works best when applied from the beginning of design, even before site selection. As the design develops, your opportunities to make more innovative green choices get fewer and fewer. The return on investment to doing an energy model, for example, after the design is already finalized and being built, is much less favorable.