In most cases deploying your website precompiled doesn't impose any problems. However, if you have a more complex structure utilizing virtual path providers you will soon run into a brick wall. So did we when trying to deploy a site yesterday.
Yesterday, when configuring a Piranha site to be deployed at City Network we ran into a classic problem. The hosting provider had decided only to support precompiled websites without just in time compilation. Of course, getting the site precompiled is only a matter of how you deploy it, but as always there's always the odd chance of something breaking.