That is an interesting idea but I don't think it will help the new tires last any longer, it may even have the opposite effect. I want to give you encouragement on this but I agree with the others here that you're best bet may be to follow the "rules" and buy a set of nice new tubes and tires, or even good used tires. I think the extra weight and awkward shape of this double tire on wheel setup will mess up the bikes performance to some degree, and could even be dangerous as someone mentioned.
It might have a purpose in a mad max style apocalyptic world where one had to work with what they had and needed tires to last longer... but even then they would need to be modified in some way to even work at all. Wheels are not designed to hold two tires. I assume theres a reason for that, it would serve no purpose....
Maybe you could fill or coat a set of tires with some sort of liquid rubber compound or even something else to make them more durable.
Good luck anyhow!