Actually the answer is NO.
The Microsoft Account you inform will be used in Games Hub for Live ID, Picture Hub for SkyDrive integration, for Me tile updates, Messages app with Messenger and Facebook and so on.
You can change the Microsoft Account your phone uses but it will change everything I mention.
Unfortunately there is no way to backup your game or app data (as of Windows Phone 8 Update 3).
According the official documentation, only the following is backed up (if enabled in Settings > Backup)
The list of apps you've installed on your phone.
Your call history.
Your theme colour.
The accounts you've set up on your phone.
Your Internet Explorer ...