>will the app be rejected in the app store review process for not having the privacy consent in info.plist?
You do know that app review isn't here and no one here can promise what they will/won't accept/reject, right?
Even if someone told you to go for it, the gate could shut before you had a chance to get near it.
That said, if you're just asking about privacy issues, have you seen that section in the ASRGs? If you're asking just about implementation liability, what do you see as your role? Trying to write a disclaimer to include with the API distribution? Looked over similar examples at github?
Otherwise, asking "should the app have to define the settings?" is pretty broad given that each app presents unique challenges to review, making it more case/by/case, than blanket, I think. If you're asking at that general of a level, the answer is always the same...when in doubt, buy the insurance.