If not universal in every action for every nation across the age of fighting sail, we can say that yes it was a pretty damn common practice.

We can even recount specific instances where the dead, thought to be or virtually dead, or parts thereof were simply tossed over in order to let the living return to their grim business. We should also make distinction here, man with his leg cutoff but alert and conscious was likely to if possible be carried below to the surgeon if some men saw him or there was a break in the action. A man unconscious from blood loss, with an arm shot away or his stomach split, and seemingly dead was possibly still alive but not long for this world and could be tossed over and some saw dust tossed down to improve traction.

This would happen even when it was clear who the dead man was, there wasn't the time, space, or ability to preserve most bodies for transport home, and the decks needed to be cleared for action.

For instance early on at that great example of Trafalgar while HMS Victory was still working her way to the Allied line she received fire from several French and Spanish ships. Several shots hit her Quarterdeck where Nelson, Captain Hardy, and other senior officers stood. One of the dead was Nelson's own Secretary John Scott. The admiral is recorded to remark 'Is that poor Scott' as his splinter mangled body was tossed over but to return to matters at hand. Sure maybe his heart was still pumping when he went over but sailors and crews had a pretty good idea of what wounds and conditions had a good chance to live and clearly dead, or appearing so when a clear deck was needed meant over the side along with any other debris on deck.

We have the following account from a seaman, Samuel Leech, aboard HMS Macedonian when she engaged the USS United States in a single ship action in October 1812. He being one of the younger members of the crew was used as a powder monkey, who ran from the Magazine to his assigned gun and back to keep her supplied and firing.

A strange noise, such as I had never heard before, next arrested my attention; it sounded like the tearing of sails, just over our heads. This I soon ascertained to be the wind of the enemy's shot. The firing, after a few minutes' cessation, recommenced. The roaring of cannon could now be heard from all parts of our trembling ship, and, mingling as it did with that of our foes, it made a most hideous noise. By-and-by I heard the shot strike the sides of our ship; the whole scene grew indescribably confused and horrible; it was like some awfully tremendous thunder-storm, whose deafening roar is attended by incessant streaks of lightning, carrying death in every flash and strewing the ground with the victims of its wrath: only, in our case, the scene was rendered more horrible than that, by the presence of torrents of blood which dyed our decks.

The cries of the wounded now rang through all parts of the ship. These were carried to the cockpit as fast as they fell, while those more fortunate men, who were killed outright, were immediately thrown overboard. As I was stationed but a short distance from the main hatchway, I could catch a glance at all who were carried below. A glance was all I could indulge in, for the boys belonging to the guns next to mine were wounded in the early part of the action, and I had to spring with all my might to keep three or four guns supplied with cartridges. I saw two of these lads fall nearly together. One of them was struck in the leg by a large shot; he had to suffer amputation above the wound. The other had a grape or canister shot sent through his ankle. A stout Yorkshireman lifted him in his arms and hurried him to the cockpit. He had his foot cut off, and was thus made lame for life. Two of the boys stationed on the quarterdeck were killed. They were both Portuguese. A man, who saw one of them killed, afterwards told me that his powder caught fire and burnt the flesh almost off his face. In this pitiable situation, the agonized boy lifted up both hands, as if imploring relief, when a passing shot instantly cut him in two. I was an eye-witness to a sight equally revolting. A man named Aldrich had his hands cut off by a shot, and almost at the same moment he received another shot, which tore open his bowels in a terrible manner. As he fell, two or three men caught him in their arms, and, as he could not live, threw him overboard.

Following the surrender of the British Frigate to her American foe he goes to help his wounded mates as best he can and recounts:

I now set to work to render all the aid in my power tothe sufferers. Our carpenter, named Reed, had his leg cutoff. I helped to carry him to the after ward-room; but he soon breathed out his life there, and then I assisted in throwing his mangled remains overboard. We got out the cots as fast as possible; for most of them were stretched out on the gory deck. One poor fellow, who lay with a broken thigh, begged me to give him water. I gave him some. He looked unutterable gratitude, drank, and died. It was with exceeding difficulty I moved through the steerage, it was so covered with mangled men and so slippery with streams of blood."

So through it all we have men who were clearly dead, and mortally wounded thrown to the sea, some with modern medicine may have survived, many probably not, but it is clear that the distinction is made that those wounds which to them stood a chance at survival would see a man sent to receive care for all the good it would do.

The full account is here: http://www.nelsonsnavy.co.uk/engagement.html