No, but he thinks another soldier did. It’s a bit of a grim tale (though that page doesn’t cite its sources, so take this with a grain of salt):

the kitten was one of two who were orphaned after a soldier shot their mother for “yeowling”. The marine who adopted the other kitten killed it after rolling over on it in his sleep.

But Praytor’s kitten survived. He fed her on meat from ration cans. After Praytor left her to return home, she became something of a mascot for the company’s public information office. Praytor believed another marine, corporal Conrad Fisher, eventually adopted her and brought her home to the United States.

Edit: this history enthusiast’s page corroborates the story with a citation of Frank D. Praytor, “The Commandant and the Cat,” The Greybeards 23, no. 3 (May-June 2009): 30-31, 65