Once you're cleared in, that paperwork should suffice while you work your way around the coast. If you have a foreign registered boat, and its obvious, you might be asked by the US Coast Guard. I doubt it, unless you've named your boat "The Wrath of Osama" or something similar...
Its no big deal if its all legit. They stop commercial boats as well, especially fishermen. They might even be helpful to you if you have questions or gear issues. Its been known to happen.