You answered your own question . There is much speculation and debate on this subject , some say yes and some say no. You are off on your dates though by a couple of hundred years , King Phillip IV of France ordered the Templars to be simultaneously arrested on Friday, October 13, 1307 (it is thought that this is where the superstition of Friday the 13th being unlucky started) . Also , it is speculated that the Templars who were in hiding started Freemasonry , not joined them .
Read John J. Robinson's "Born In Blood" . He claims to have found ties between the Templars and Freemasonry , but I think it is nothing more than speculation . I for one do not think it is true , but the next Mason may post that they do think is true . No one person has a definitive answer , you will have to do your own research on the subject and draw your own conclusions as to weather if it is true or not .