If it was cooked already and then put in the fridge I dont see why not. Everything has already been cooked on it.
They say to heat it up because listeria can come back when things cool down. So I heat mine up just to be safe, and it has to be really warm to kill it so the hotter it is the better.
I do! It's funny cause I asked my doctor about that and you can! Just like you can eat sushi if the meat in it is already cooked :)