No, they had nothing to do with one another. The Turkey Shoot took place when the U.S. was taking back the Marianas Islands. Saipan, Tinian and Guam. June of 1944. Leyte Gulf took place the following October after MacArthur landed in the Phillipines.
And, I too, think that the Battle of Leyte Gulf, which is actually several battles, is one of the most fascinating fights of the Second World War.


"From our orbital vantage point, we observe an earth without borders, full of peace, beauty and magnificence, and we pray that humanity as a whole can imagine a borderless world as we see it, and strive to live as one in peace."
Astronaut William C. McCool RIP, January 29, 2003 - Space Shuttle Columbia