Can the Philosophy thought game "The experience machine" be answered by Positive Psychology?
The experience machine is meant to be an argument against hedonism in that it's supposed to show that humans value other things than happiness and therefore wouldn't/shouldn't hook themselves up to the machine (whether it succeeds in doing this is another matter; Nozick simply points out that it would be "absurd" for anyone to connect oneself to the machine, an in my opinion extremely weak argument). 

As such, the machine in the thought experiment is meant to supply you with whatever experiences that will create the largest amount of happiness for you (however, it's never explicitly stated that the experiences would have to be happy experiences; it's simply stated that the machine would be able to supply you with whatever experiences you desired, and when addressing a hedonist, those experiences would be happy experiences). If this means that you need a big chunk of sad, soul crushing experiences from time to time just to be happy the rest of the time, then so be it; as long as there is some pattern of experiences that in the end would generate more happiness for you than what you would experience in real life (a.k.a your real life isn't perfect), the thought experiment applies.

So, regarding your last question, the thought experiment really is immune to the kind of objections that you bring up, which means that we can't be informed about the solution to it by empirical research.

With that said, the question of how much and what type of negative experiences, if any, we need to be able to experiences happiness is interesting, but I don't have the answer to that one. 

(Random speculations mode commencing: However, in my view, this seems to be more of an assumption that people make rather than something that is firmly based in science. Do we have the same intuition when it comes to pain? Would we say that a person who was raped and tortured since birth wouldn't be worth rescuing since she because of the lack of positive experiences didn't experience any negative experiences? Is there a reason to believe that this alleged relationship between positive and negative experiences isn't symmetrical?)