No, unfortunately. Royal Mail’s Click&Drop Support Team have confirmed it currently cannot be done and after I posted this same question on their forum (https://clickanddrop.uservoice.com/forums) my post was removed!
It’s very frustrating as every other detail gets pulled through and setting up postage rules in Click&Drop doesn’t help us.
Ah well. To be fair I am just delighted that it connects to shopify at all, as we were with Wix until recently and everything had to be exported, imported etc. So it’s a step up for us already.