I'm afraid this answer may not fully satisfy you, but in the most basic terms, we don't really know.
The way that service aboard ships worked in this era for common sailors is that they formed part of a ship's company for one commission, or voyage (although the definitions of both are a bit loose -- basically, the time from which a ship's company was formed and its officers appointed until it was "paid off."). There wasn't anything like what we have today -- if you walk down to your local Navy recruiting office, you're signing on for four years active duty and two years reserve duty, and put wherever the Navy needs you.
In the 19th century, nothing like that existed, which means we don't have anything like a list of all seamen serving in the American or Royal Navy, much less a list of men who would have been involved in merchant service (who were mostly the men the RN was impressing during this time). There were some citizenship documents issued by local authorities, but Britain claimed that birthright citizenship overrode naturalization citizenship, and anyhow the US government didn't have much interest in issuing official citizenship documents to sailors. Albert Gallatin estimated that half (9,000) of the men working in American merchant ships were British subjects, and if he and Jefferson were to issue official papers to merchant seamen, half would naturally have to be given up to Britain if it asked.
The range for the total number of American seamen that were impressed in the lead-up to the war varies pretty widely depending on the source, with so-called "War Hawk" printers seizing on an 1812 report from Secretary of State James Monroe that 6,257 Americans had been impressed since 1803, while Federalist papers estimated the total number at only 10 or a dozen. in 1813, the British Foreign Secretary Lord Castlereagh (Robert Stewart) estimated that about 1,600-1,700 Americans had been impressed, and after the war Britain released about 1,800 seamen from the Royal Navy who claimed American citizenship. (The end of the War of 1812, of course, also coincided with the end of the Napoleonic Wars and the drawdown of the RN in general.)
I have answered a couple of previous questions about impressment, which are gathered here, if it's of interest for you.