The Mach 1 comes with the gt350 airbox as oem. No, you do not have to get a different tune if you are just changing the airbox to a gt500 one if you have a Mach 1.
Just took a picture of my engine bay. The red cobra is a homage to all of the parts the Mach 1 "borrowed" lol I changed out the GT350 OEM airbox with a GT500 airbox. Changed out my Mach 1 strut tower brace to the GT350R strut tower brace.