No. MLB 09: The Show was never released on Xbox 360. The entire MLB: The Show series has been a PlayStation exclusive since its debut in 2006 (PS2/PS3), continuing through PS4, PS5, and (since 2021) Xbox Series X|S—but never on Xbox 360.
If you're on Xbox 360 and want baseball, your options are:
The Show didn't come to Xbox until MLB The Show 21 on Xbox Series X|S (via MLB's licensing deal). No 360 version exists.