Yes, what Scylla said and it is a known possible risk with freediving called a “shallow water blackout.”
First recapping the background. The main drive to breathe is increasing levels of CO2 (hypercapnia), not decreasing levels of O2 (hypoxia). But it is the hypoxia that will result in passing out, not the hypercapnia. Under normal circumstances the CO2 drive forces a breath before hypoxia results in passing out.
Some freedivers will hyperventilate before a dive to get CO2 levels way down before the dive (in hopes of prolonging their time) with the result that hypercapnia does not trigger the end of the dive before hypoxia results in a black out.
If you want to see it happening there are youtube videos of episodes available.
Some years ago I saw a video in which Nick Nolte did the exact same thing. Empty your lungs (very) completely, and you start sending unoxygenated blood to your brain; it happens too fast for CO2 to build up and cause air hunger, so you pass out without much agony.
When my sister was a toddler, she used to cry like this too. At some point she would exhale so long and forcefully that she would pass out - and then resume consciousness a few seconds later, much like a befuddled Nick Nolte.
Low oxygen in the blood going to the brain is not likely what is going on with Nolte there and not the main mechanism of childhood breath holding spells. Low enough oxygen does not happen that fast. The main mechanisms there are generally believed to be blood flow in origin and include an overlarge vagal reaction, decreased venous return, and brain blood vessel reaction to low CO2.
You can best think of the vagal (parasympathetic) response as the ying to the sympathetic’s (“fight or flight”) yang. It, among other things, lowers heart rate and blood pressure. There are a variety of areas that have receptors that when stimulated activate that response, including in an area of the arteries of the neck (the carotid bodies). That’s why that massaging of those neck arteries can cause fainting. (Makes sense for the body to interpret an increase in perceived pressure there, going to the brain, as something to trigger a decrease in blood pressure response.) Straining, crying hard, hyperventilation, pain … all are strong triggers of that response. Heart rate slows, blood pressure drops, and the brain just does not get enough blood flow so the child (be it a preschooler or the man-child that is Nolte) passes out.
Another factor in kids in some cases may be the pressure on the superior vena cava from a very large pronged inspiration which decreases blood flow into the heart at the same time. Less blood in means less blood out …
The brain blood vessels also react to low CO2 (the result of hyperventilation) by constricting, obviously also decreasing brain blood flow during hyperventilation.