Most definitely, since this is a behaviour that annoys people and has an apparently unpredictable pattern (in reality, it's just that the partition is encrypted, but nothing prompts the user), this must be fixed.
So either you say "look, your backdrop is not going to be shown in the greeter, which will show the standard one" or you just take the plunge and copy the backdrop to /usr/share/something and let the damn thing bring it up.
Most definitely, since this is a behaviour that annoys people and has an apparently unpredictable pattern (in reality, it's just that the partition is encrypted, but nothing prompts the user), this must be fixed.
So either you say "look, your backdrop is not going to be shown in the greeter, which will show the standard one" or you just take the plunge and copy the backdrop to /usr/share/ something and let the damn thing bring it up.