Not exactly. Acceptance of a driver license comes with implied consent. Implied consent is specifically applicable to DUI testing. It depends on which state you're in, of course, but generally, you can decline a breathalyzer test, but not a blood test. You may accept a breathalyzer in lieu of a blood test. If you fail the breath test (these things can be fooled by how recently you've consumed), then you can demand a blood test, which is the true measure of blood alcohol level.In point of fact, it is. For the same reason that refusing a breathalyzer test is the same as failing the test.
In NV, there is no implied consent, so LEOs actually need your permission to take your blood.
The point is, driving on public roads is not a right protected by the Constitution. The argument around coolers and campsites would more appropriately be focused on the issue of reasonable expectation of privacy. If it's locked, for example, there is a clear expectation of privacy.
IMO, a campsite that is clearly not abandoned SHOULD also qualify for an expectation of privacy, even if noone is in the immediate vicinity. Whether it does or not is up to a judge (but it shouldn't really get that far, IMO). If you have a way to lock your tent, then expectation of privacy should hold up (unless there is some other law in effect such as implied consent for your hunting license or using campgrounds, etc... which would be dumb).