No he is not a heartless. Because his heart resonated with Kairi's and brought his heart back to his body. If he were a heartless then he would be a hero of Darkness not a hero of Light. Remember the Heartless are creatures of Darkness, Sora is a being of Light. So its not that he has no heart, his heart was too full of light to be tossed into the darkness, allowing him to regain himself compleatly. Rembmer too that most heartless cannot thing for themselves, and if you recall Xehanorts heartless didnt really think about all that much, he mostly thought of what was instinctual to most heartless. Find other worlds hearts and feed them to the great heart. Kingdom Hearts.
Sora makes his own decisions and what not so I dont think there is anyway that he is a heartless.