I'm pretty sure that's not the case on water the CG manages. I believe they can inspect your vessel at any time. In addition, I'm also pretty sure that the DNR can pull you over and have you show them that you're properly equipped, ie. enough life jackets, throwable cushion, fire extinguisher, etc. I would think them checking your capacity plate would also be with in their jurisdiction to check.
That would be different from the 4th Amendment to an unlawful search...they can't just start looking in storage areas.
Also, the analogy with a suped up car doesn't really work. If the car's engine breaks off its mounts, no one sinks. On a boat, you're in serious trouble instantly.