In Australia every CPDLC communication I've had has always been backed up with VHF communications from the ATSU in question. Seems pretty pointless using it in Australia when you have VHF contact, maybe the controllers are just bored. Using CPDLC and VHF comms seems to increase pilot workload rather than reduce it.
It's great using it in India where HF comms can be difficult.
At the end of the day you can always log on in order to establish communication if you're experiencing difficulties with HF. If you're not sure about whether your company wants you to use CPDLC then you can always reject any instructions/commands offered and don't ask for any yourself.