Can You Download Xbox 360 Game Patches on PC and Transfer Them?
No, you cannot download Xbox 360 game patches on a PC and move them to the console.
Why
Console-Tied: Patches are built for the console's specific hardware/software.
DRM Protection: Patches are encrypted and tied to Xbox Live; cannot be transferred from PC.
Xbox Live Delivery: Updates are delivered automatically via Xbox Live when the console is online.
How to Update Properly
Connect Xbox 360 to internet.
Ensure system software is up to date (Settings > System > Console Settings > System Info).
Launch the game; it will auto-download/install available patches.
Note: Some games require the disc inserted to download patches, even for digital copies. Check Xbox Live or the game's official site for specific issues.