IF AND ONLY IF you know that the object is either a true or fake oracle: you can determine that it is oracular for all programs of some finite length X, where X is determined by the amount of time you want to spend feeding in n-length programs known to halt.
For any given X, you've identified that the oracle is true for X or less, but you cannot confirm that X > N, and thus cannot confirm whether the oracle is true or fake, simply that it will be true for all lengths X or less.
That said, if your goal is to evaluate program A, you can just run a known-halting problem of the same length past the oracle to confirm that it's valid for evaluation of this program. If you do this for each program you evaluate, then your results become "halts", "doesn't halt", "this is actually a fake oracle, oops", with 100% confidence :)
(I realize 100% confidence should never exist, but if there is the possibility of it being a true oracle, a fake oracle, or a different sort of fake oracle, then NONE of these conclusions is valid. So we get to play with a hypothetical super-certainty world where there's only true and fake oracles :))
I feel this is a bit of an artifact of the problem statement though -- I feel a more "realistic" scenario is that we are given a block box which which is either an oracle, or is correct for programs <N and returns arbitrary answers (sometimes correct, sometimes not) for longer programs.
Here's something I've been wondering about, in the context of Solomonoff induction and uncomputable sequences.
I have a device that is either a halting oracle, or an ordinary Turing machine which gives the correct answer to the halting problem for all programs smaller than some finite length N but always outputs "does not halt" when asked to evaluate programs larger than N. If you don't know what N is and you don't have infinite time, is there a way to tell the difference between the actual halting oracle (which gives correct answers for all possible programs) and a "fake" halting oracle which starts giving wrong answers for some N that just happens to be larger than any program that you've tested so far?
The Kolmogorov complexity of an uncomputable sequence is infinite, so Solomonoff induction assigns it a probability of zero, but there's always a computable number with less than epsilon error, so would this ever actually matter?