How's that even possible?
The Ming would never allow Hideyoshi to conquer Joseon, and it had the means to quash his forces. Joseon itself could have fended them off at sea on the onset of the Imjin War, though to the Japanese fleet's good fortune, the Korean admiral in charge was a total dunce and sat by to watch them unload their armies on Korean soil. After which, he promptly had the fleet scuttled when they overran the area.
Even removing Yi Sun-Shin from the picture and having Joseon's military run by idiots won't do much to improve Hideyoshi's chance of getting an annexation. It was just a matter of time before his luck ran out and reality sets in in the form of the Chinese.