Some airlines may allow wrapped packages in checked luggage as long as they've been through an x ray machine to determine what is in them.
However some airlines may want the packages unwrapped and will unwrap the packages to see what is inside them personally.
It's best to leave the presents unwrapped when traveling by plane and then wrap them when you get to your hotel or wherever you plan to be.
It's certainly up to the airport but to save yourself some headache just leave the packages unwrapped and wrap them when you get to the destination.