Will a shade sail have too much pull on 4x4x12' posts?
It isn't a question of post size. Well, it is, but you have bigger concerns: The brackets will not serve your purpose. They're mostly designed to anchor the base of the post, and to keep it off the concrete. They don't provide nearly enough stability to keep a post standing under load. 

Your posts must be embedded a substantial distance into the concrete. 1:3 is a good rule of thumb for anything carrying lateral loads. (Heck, the concrete does nothing at all for you in your scenario.) Or they must be supported with rigid crossbars or diagonals of adequate length.

If your posts will actually be 12' above ground, and they're not supported with any sort of diagonal bracing, you will want 6x6s (or at least 4x6s). 4x4s will flex and bounce substantially at that height.