I think you're asking whether a t-test is appropriate when your data consists of a binary response, i.e. a Success or a Failure, and you've got a very small number of responses. If so, the answer is no it isn't: it seems to me you ought to be looking at some sort of permutations test for a situation like that; that is, work out all the various possible outcomes, and then see how extreme the one you've actually got is. Sorry I can't be more specific than that: I'd need to know more about the actual data.
