This is speculation on my part:
The frozen turkey shouldn’t be any worse than the items normally put directly into the fryer. Frozen wings, fries, etc. are routinely dropped into the fryer, as intended. The initial sizzle is caused by water rapidly boiling off, but the amount of water available is relatively limited so the boiling is at a safe level. When you throw water into the fryer there is lots available all at once, it expands rapidly and sprays oil everywhere.
The dry ice would similarly sublimate very rapidly, expanding rapidly, and shooting oil everywhere. A quick google shows the density of dry ice at 1.6 g/cm3, vs. cooking oil at about .92g/cm3. So the dry ice would sink, expand rapidly at the bottom of the oil, and spray molten death like confetti.
ETA: Most commercial fryers I have seen use an electric heating element submerged in the fryer, so flames are not a concern. Backyard propane setups do have open flames.