Can "Conch Republic" passports actually be used for anything?

Border policies for non-immigrant visitors are generally established by reciprocally-negotiated treaties or other less-impressively-named international agreements among the participating nations. So as a matter of formal policy, no country is going to take it seriously.

That being said, Slashdot is a hangout for hackers and engineers, any one of whom could probably explain to you the concept of "social engineerng" - the art of manipulating people toward a desired end. Ultimately it is a question of whether the person(s) reviewing your passport are going to accept it as valid or not. Skillful social engineering could skew that chance heavily toward the "Yes" column.

But you have to consider the potential downside risk if your passport is recognized as a fraud. Depending on the country of destination, I'd be afraid of suffering everything from a heavy fine to prosecution for fraud to imprisonment as a potential spy.

There are plenty of world nations that will let you buy, work, wait, or suffer your way to a legitimate second passport. If I genuinely felt the need for one, that's the way I would go. Much less downside risk.