Potentially. It depends on how you read and look at the rules. Even assuming that's the case, your new minion will then immediately need time to recover or be pretty much useless until it does. Also, see the other thread for reasons why this is usually a bad idea. Two words: Diplomatic Repercussions.
Though now that I think about it, there's also the whole 'literal genie' problem, where your new minion is ordered to protect you from the demon, and immediately kills you since then the demon can't. That's a bit of an over-the-top example, but the kind of thing that's likely to be a much bigger problem for powerful creatures than the less powerful.