I believe 2178.5 KHz has been discontinued but may still monitored in limited fashion. Below are the HF Distress DSC frequencies that the CG monitors.
HF DIGITAL SELECTIVE CALLING
Portsmouth/NMN, Boston/NMF, Miami/NMA, New Orleans/NMG, Pt. Reyes/NMC, Honolulu HI/NMO, Kodiak AK/NOJ
4207.5 DSC test calls on 4207.5 KHz will be automatically acknowledged from Portsmouth/NMN and Pt Reyes/NMC. Responses to test calls on other frequencies and at the other locations may be delayed and cannot be assured.
6312
8414.5
12577
16804.5
Note: For digital selective calling, frequencies listed are assigned.
Carrier frequency is located 1700Hz below the
assigned frequency.
Unlike VHF which assigns Channel 70 as the distress DSC channel, HF can use any frequency. However, there are assign HF frequencies that are guarded (monitored) by the USCG (4125, 6215, 8291, 12290) and other worldwide SAR agencies. All these are by international treaty and all will respond to the distress call.
Any boater can use DSC to call another boat using either VHF or HF. DSC is just not for distress. It is like a telephone number for you to call your buddy who is local (VHF) or on the other side of the world (HF).
To activate distress DSC on VHF just press the button and it will automatically select channel 70. On HF, I believe you have to select the desire distress frequency (6, 8, 12, or 16 MHz) and then press the button. I am not 100% sure of the process on HF.
To answer the original question, a separate antenna is not required for DSC use on HF. The HF antenna is a broadband antenna with the use of a tuner. I would recommend that you monitor the selected HF frequency that is appropriate for the location you are sailing and set the radio for that location. You will have to understand how HF propagation works to ascertain the correct frequency of the area you want cover. Makes no sense to monitor a frequency that will allow you to receive DSC from the Pacific if you are in the Atlantic.