How can I determine if just the .private folder is encrypted or the whole home directory?

From the terminal type:

cat /home/.ecryptfs/$USER/.ecryptfs/Private.mnt

If the file exists and contains your home directory path, your home directory is encrypted.

Another way to check is looking at your home dir mount point:

From the terminal type:

df $HOME

An encrypted home will be mounted at the ".Private" filesystem, otherwise it will be mounted at some regular partition device (/dev/*) .

Filesystem           1K-blocks      Used Available Use% Mounted on
/home/username/.Private
                     315482376 101351268 198105472  34% /home/username

Regular device mount (no encryption):

df /home/schroot
Filesystem           1K-blocks      Used Available Use% Mounted on
/dev/sda7            315482376 101351332 198105408  34% /home

This is a great question! It actually comes up a lot, from a programmatic perspective. Programs, processes, and applications like the Ubuntu installer, lightdm, and gdm actually need to know if $HOME is encrypted, or Private, and if they're set up properly.

I've recently written a utility, ecryptfs-verify-private, that was be released in the eCryptfs release version 96.