To be fair, I think "do you have them?" would be more common for a lot of English speakers ("have you got" sounds British to me as an American, but it's possible that this is just a regional American thing). I'm not sure I would either think fast enough to care enough to tailor my automated response to a question like that based on the exact phrasing of the query.
Americans still use it as a response though, e.g. "You got this!" - "I do!". it's the "I do got" which really bugs me. "I do have" and "I have got" are fine and make sense