Greetings and thanks for the post! I've been doing some further research in regards to this (I was curious as well) and it looks like Facebook Home is available on the HTC One X+ device which is not currently available for Sprint.
If I hear anything further, I'll let you know!
Sprint Social Care Team
"Get Facebook Home on your own Android in 3 steps. Add the Messenger and Facebook apps for the full experience. Facebook Home for Android is available for download from the Google Play Store on certain devices, including the HTC One X, HTC One X+, Samsung Galaxy S III and Samsung Galaxy Note II"
quote taken directly from bottom fo the page at www.facebook.com/home
can Sprint contact Facebook and get this opened up?
EDIT: Downloading the .apk and installing us a no go as well. App does not recognize the device.