Last time I was forced to gate-check luggage (no overhead compartments, just shelves) and was promised it would arrive at my destination with me - they lied. Not just to me, but to all the passengers whose luggage was supposed to be placed inside the luggage/cargo area.
Of course, this was after the airline lied about the reason for the extreme delay at connecting airports - snow in Boston on what turned out to be a 100% clear, precipitation-free night.
Please don't expect this. If you want your child to have a seat, please purchase a ticket. Many airlines will not allow an unticketed* passenger to occupy a seat; some will but only if there is seating available for every single unticketed passenger. Also please don't expect someone to move to a different empty seat to accommodate your wish to put your son in his carseat if you did not pay for a seat for him.
And please don't attempt to make that passenger's ride difficult or uncomfortable if they refuse to comply.
*unticketed = child under age two