He would have bled to death if Tomoyo & co wouldn't have been conveniently there to attend him asap when he reached Japan. Of course, they were there to attend him because Tomoyo had already arranged with Yuuko for everyone to go to Japan after Celes and she was the one who told Kurogane the method to bring Fai with him. Tomoyo knew he would come to Japan severely injured and prepared so they could save him.
