Is it really possible that a man could have a penis so enormous that he would pass out when hard?
No.
"But but but…" you say. And again, I say "No." Let's talk anatomy. Specifically, let's talk blood.
The average adult male's body contains around 10 pints (160 fl oz / 5 liters) of blood. That blood is constantly pumping through every part of the body, coursing out from the heart through arteries, and returning deoxygenated via veins. When you donate blood, you typically give up a whole pint (16 fl oz / 470mL), or roughly 10% of your total blood volume. A healthy man is able to function perfectly fine with that level of blood loss, so long as they stay hydrated and eat well.
It takes a lot more blood loss to start causing problems. It's medically accepted that a blood loss of 15-30% of total volume is the line where things go south. This is considered to be a Class 2 hemorrhage, with symptoms including lightheadedness, weakness, and paleness.
How does this apply to penises? The average penis grows from a soft size of 3.5 inches long and 3.5 inches around to an erect size of 5.5 inches long and 4.5 inches girth. That's a volume increase of 260% from flaccid to erect. That erection is achieved [entirely by pumping blood into the corpus cavernosum and corpus spongiosum tissues, for an average dude that's roughly 4.4 ounces (130 mL) of blood to sustain his erection.
That blood isn't removed from circulation; it's still flowing through the penis, just more of it is backed up inside the dick at that moment. Technically it's not helping with other circulatory functions like supplying blood to the brain, so in effect that does reduce the volume of blood available to run the rest of body.
For the purposes of this exercise, let's say our guy gets lightheaded at 15% blood loss, which means we need to remove 24 oz (700 mL) of blood from circulation — in addition to the blood that's normally flowing through his flaccid penis. With an average 260% growth percentage, that means our guy is starting with a soft penis that has a volume of 9.2 oz (270 mL). Dimensionally, that's a soft penis that measures 7 inches long and 5.75 inches girth (17.5×14.5 cm). Again: enormous soft dick.
Now we need to grow its volume by 260% to sequester an additional 24oz of blood from our guys arteries. To get a 33 fl oz (975 mL) dick we need some ungodly dimensions.
For a healthy man to pass out from an erection he needs to have a penis that is 13 inches long and 8 inches around (33×20 cm).
Alternative dimensions include 17×7" and 10.5×9". Regardless, we're well into the realm of impossibly large penises (especially if you don't count the faker Jonah Falcon).
So no, it is not possible for a man in good health to suffer from lightheadedness from achieving an erection in his enormous penis. If you are getting lightheaded or passing out when you get hard, something's not right. You might be dehydrated, malnourished, exhausted, overwhelmed by hormones, or in very poor cardiovascular fitness.
Those with heart conditions, diabetes, and other circulatory system ailments could experience lightheadedness in conjunction with erections, but that's correlation, not causation, and can happen with a penis of any size. When you're aroused, your heart beats harder and hormones are released into the blood stream. If you're in poor cardiovascular health then all that excitement can cause lightheadedness. If you correct for the controllable factors like diet and exercise and are still getting faint when you're getting hard, then it's time to talk to your doctor.