Hi!
With your question on the Sprint GT you'll need to ask the experts. I loaded Gingerbread 2.3.3 on my GT International free version, from the UK, rooted it, and it is working perfectly! I love it...
I tried three versions of how-to's and gave up on the first two, as they were confusing and incomplete. I suggest using this one:
How To Install Android 2.3.3 Gingerbread ROM On Samsung Galaxy Tab
However, even this one is incomplete, as it leads you to believe that you will download and extract all the files needed, and it doesn't.
I suggest first searching for the dbdata.tar file in Google, and downloading it to extract on your desktop.
The addictivetips directions will also eventually give you the following .tar file if you select the version with bootloader:
P1000XXQ1_P100XXJQ1_P1000XXJPZ_home.tar
Odin will need both of those .tar files, as well as the other .pit files on your desktop, but only on a temporary basis.
I also suggest that you make sure that your device is updated with current, appropriate device files. I downloaded the Galaxy-S files as suggested, and couldn't get my GT to be enabled. So, I loaded Kies and updated my files with their update program, and it worked. You'll need your GT to be enabled, for Odin to have the ID:com tab turn yellow, confirming that the device files are loaded properly.
Don't forget to turn off your Kies program.
Also, make sure that you are using ODIN7 v1.7, instead of ODIN v1.3!
If you are having trouble getting into the Download and Recovery modes, be sure to release the buttons on your GT, as soon as you see the Galaxy logo.
Now that you are an expert on using Odin, you can use that expertise by using the other addictivetips directions on the same page, using the How to Root your GT link it provides.
Okay, let's give it a try!
Work slowly, work carefully, get organized, and you'll be okay!
I hope this is helpful to you, and for any others trying to update their GTs to Gingerbread!
Let me know how you make out!
Good luck!
Golf Educator