Eric, I don't know of any GBCI or LEED requirement that would prevent you from doing this.
I don't think it's advisable, though. From people I have talked through who have been through projects like this, e.g. starting LEED when construction is about to start, not even when it is completed, it is a tough row to hoe.
Think of all the documentation you have to track down after the fact, all the people who will have to cooperate, and there may be data gaps that you can't fill.
All this, for what benefit? LEED is best used when it can influence the direction of design and construction.