‘Fawkes is a phoenix, Harry. Phoenixes burst into flame when it is time for them to die and are reborn from the ashes. Watch him ...’ Harry looked down in time to see a tiny, wrinkled, new-born bird poke its head out of the ashes. It was quite as ugly as the old one.
Aqui parece que Fawkes surge de uma pilha de cinzas, mas
Fawkes swooped down in front of Dumbledore, opened his beak wide and swallowed the jet of green light whole: he burst into flame and fell to the floor, small, wrinkled and flightless.
Aqui vemos que Fawkes morre e renasce imediatamente no ar, enquanto cai, então sua pilha de ashe provavelmente está espalhada.
Baseado nesta citação, parece que nada aconteceria se você tentasse mover ou separar as cinzas, e desde que a fênix renasceria imediatamente, você realmente não teria tempo de "parar" o renascimento mexendo com as cinzas de qualquer maneira.
Nota lateral, fênix não é imortal,
The phoenix lives to an immense age as it can regenerate, bursting into flames when its body begins to fail and rising again from the ashes as a chick.