I am going to say no.
As a previous answer has stated drowning is due to lack of oxygen to the brain and ultimately the brain dies.
Drowning is defined as respiratory impairment from being in or under a liquid. Also as wiki states in classified as death, ongoing health problems and no ongoing health problems.
Oxygen deprivation A conscious person will hold his or her breath (see Apnea) and will try to access air, often resulting in panic,
including rapid body movement. This uses up more oxygen in the blood
stream and reduces the time to unconsciousness. The person can
voluntarily hold his or her breath for some time, but the breathing
reflex will increase until the person tries to breathe, even when
submerged.
The breathing reflex in the human body is weakly related to the amount
of oxygen in the blood but strongly related to the amount of carbon
dioxide (see Hypercapnia). During apnea, the oxygen in the body is
used by the cells, and excreted as carbon dioxide. Thus, the level of
oxygen in the blood decreases, and the level of carbon dioxide
increases. Increasing carbon dioxide levels lead to a stronger and
stronger breathing reflex, up to the breath-hold breakpoint, at which
the person can no longer voluntarily hold his or her breath. This
typically occurs at an arterial partial pressure of carbon dioxide of
55 mm Hg, but may differ significantly from individual to individual
and can be increased through training.
The breath-hold break point can be suppressed or delayed either
intentionally or unintentionally. Hyperventilation before any dive,
deep or shallow, flushes out carbon dioxide in the blood resulting in
a dive commencing with an abnormally low carbon dioxide level; a
potentially dangerous condition known as hypocapnia. The level of
carbon dioxide in the blood after hyperventilation may then be
insufficient to trigger the breathing reflex later in the dive and a
blackout may occur without warning and before the diver feels any
urgent need to breathe. This can occur at any depth and is common in
distance breath-hold divers in swimming pools. Hyperventilation is
often used by both deep and distance free-divers to flush out carbon
dioxide from the lungs to suppress the breathing reflex for longer. It
is important not to mistake this for an attempt to increase the body's
oxygen store. The body at rest is fully oxygenated by normal breathing
and cannot take on any more. Breath holding in water should always be
supervised by a second person, as by hyperventilating, one increases
the risk of shallow water blackout because insufficient carbon dioxide
levels in the blood fail to trigger the breathing reflex.
A continued lack of oxygen in the brain, hypoxia, will quickly render
a person unconscious usually around a blood partial pressure of oxygen
of 25–30 mmHg. An unconscious person rescued with an airway still
sealed from laryngospasm stands a good chance of a full recovery.
Artificial respiration is also much more effective without water in
the lungs. At this point the person stands a good chance of recovery
if attended to within minutes.
A lack of oxygen or chemical changes in the lungs may cause the heart
to stop beating. This cardiac arrest stops the flow of blood and thus
stops the transport of oxygen to the brain. Cardiac arrest used to be
the traditional point of death but at this point there is still a
chance of recovery. The brain cannot survive long without oxygen and
the continued lack of oxygen in the blood combined with the cardiac
arrest will lead to the deterioration of brain cells causing first
brain damage and eventually brain death from which recovery is
generally considered impossible. The brain will die after
approximately six minutes without oxygen but special conditions may
prolong this. Obviously there is some magic involved in Percy being
able breath under water and as another answer states, he probably has
some mechanism that enables him to get the oxygen from the water.
As for Hyperventilation, this is what Wiki state on Hyperventilation
Hyperventilation occurs when the rate and quantity of alveolar
ventilation of carbon dioxide exceeds the body's production of carbon
dioxide.1 Hyperventilation can be voluntary or involuntary.
When alveolar ventilation is excessive, more carbon dioxide will be
removed from the blood stream than the body can produce. This causes
the concentration of carbon dioxide in the blood stream to fall and
produces a state known as hypocapnia. The body normally attempts to
compensate for this metabolically. If excess ventilation cannot be
compensated metabolically, it will lead to a rise in blood pH. This
rise in blood pH is known as respiratory alkalosis. When
hyperventilation leads to respiratory alkalosis, it may cause a number
of physical symptoms: dizziness, tingling in the lips, hands or feet,
headache, weakness, fainting and seizures. In extreme cases it can
cause carpopedal spasms (flapping and contraction of the hands and
feet)
What eventually happens is you most likely pass-out due to the easiest way to get oxygen to the brain is on the floor and the body use involuntary reflexes to return the bodies breathing to a state where it can survive. I don't know how many documented case of people dieing from hyperventilation, but it is very small and there usually is complications.
So, going back to Percy, even if he were to panic, he would eventually pass out and his involuntary reflexes take over to resume normal breathing and as he is able to breath under water, he would then therefor not die.
Resources, I am a medical physician.
