Not a huge amount. By 1805, after Trafalgar, France's navy was essentially eliminated as a serious threat. Had it taken the Danish navy in 1807 it might have recovered somewhat, but the British had a plentiful opportunity to snuff out that chance by doing the OTL thing and destroying it in harbour anyway. Nelson had scandalised British society with his public affair with the Ambassador to Naples' wife, and he had become an outcast in society. He was beloved by sailors in the RN, but when he took shore leave in 1803 he came under so petulant attack by the people of England that he was forced to stay in the home of another man marked out for sexual indecency, as he had no home and everyone he turned to refused to allow him to stay. He was already eyeing up retirement. Chances are he'd stay in the navy, possibly past the Battle of Copenhagen 1807, and then retire before the end of the Napoleonic Wars, using his service and his pension to bully the Admiralty into buying him a house where he could retire and essentially forever stay out of the public eye. Chances are that even if he lived another 20 years, the history books would never hear from him again. By all accounts he just wanted to find somewhere where he could escape from the world with Emma and his newborn child Horatia.