Gravy: NO. Sadly, you can't bring gravy in your carry-on unless you follow liquid policies. But you can pack it in your checked baggage.
Cranberry sauce: SEE ABOVE.
Pie: YES. But it may need additional screening.
Mashed potatoes: YES. Instant potato flakes are considered a solid, so that's okay to take on board. Already-made mashed potatoes needs to be packed in a checked bag because it's considered a gel.
Beverages: YES. Wine, liquor, beer and all of your favorite beverages are allowed in your checked baggage. You can also bring drinks packaged in 3.4 oz or less bottles in your carry-on in the liquids bag. But that doesn’t mean that you can indulge on the flight. According to FAA regulations, you can only drink alcohol if you are served on the airplane.
Turkeys: YES. TSA says you can actually bring it along in your carry-on. But if your turkey is packed with ice in a cooler, the ice needs to be totally frozen when it's screened. Otherwise, it's considered a liquid and won't be allowed.
Turducken: YES. You can pack it in both carry-on and checked bags. Turduckens can be packed in dry ice for carry-on and checked bags.
If you pack your turducken in regular ice, remember that the ice must be completely frozen when going through the checkpoint in order to adhere to the 3-1-1 rules for liquids, gels and aerosols.
And last but not least, odds are a turducken in a cooler (or shipping box) might exceed your airline's carry-on size allowance, so make sure you check with them before you go to the airport.