It depends on where the DND is being applied.
If the DND has a code that is being sent to the UCM or other PBX, the UCM, upon seeing the code, is the one that is responding. At this point the DND is being handled at the UCM level and no calls will be sent to the extension. The phone has no pre-recorded voice prompts. You can look in the web interface of the phone and see if the DND settings have been populated with the codes that are applicable to your PBX or provider.
If the DND is applied at the phone, then the phone is managing and will send a 486 response to every INVITE. The issue might arise that when the DND is at the phone, it may “chirp” like it is starting to ring, but then realized that DND is applied and will stop.