The A&H records at 48khz (or 96k). I use Nuendo which is essentially Cubase. You must create the Cubase project as 48k and also make sure the Cubase ASIO settings for your audio interface is also set to 48k, unless you are using the CQ as the audio interface and it will be at 48k already. Once you have done that, you can bring the tracks into Cubase or record them in from the CQ. If you don’t set Cubase and the project up correctly beforehand it will probably give you problems with mismatched audio sample rates. It’s hard to say what Melodyne as a plugin would make of that.
I have not tried Melodyne with any of this, but I’d be safe and keep the audio and Cubase Project at 48k – why not? If you need to convert to 44.1 to burn to a CD or whatever, do that after you have mixed down to stereo.