Anything is possible in the USA, look at OTl, Donald Trump is POTUS. Also, the USA has had Presidents who came from humble beginnings such as Lincoln and Truman who also were compromise candidates.
For Pulaski, need him to survive the war, OTL he was killed in the battle for the Americans to retake Savannah, GA. His porn stache lives on though.
That leaves Kosciuszko as the lone Polish hope for POTUS. For him, he made friends easily with Americans of importance due to his skill as a combat engineer and devotion to the American cause. Have him stay in the USA after the war to help build the nation. Have his American friends encourage him to stay, that the battle for freedom has just began. I do not know if he was married before arriving to the USA, but meeting an American gal would want to make him stay more. Have him turn to politics, first state and then national. Have him maintain and build friendships in the political realm. One interesting thing that he stood for, was equality for all people regardless of skin color. That would be awesome to have him in American politics with those views. Even if he does not become POTUS, he will undoubtedly touch the lives of more Americans in a positive way.
Similar question, would the Marquis de Lafayette be a candidate for POTUS if he remained in the USA as well,