There are all chances that Camilla will reach the same level of affection and popularity, as the Nation's granny. We have no idea. In the Netherlands, Belgium, Spain and in the Vatican there are new monarchs and new consorts. It is surprising how quick the old guard seems "forgotten": Beatrix, Albert II and Paola, Juan Carlos and Sofía, Benedictus XVI... all still around, all part of history.
It already feels "natural" to see the new monarchs and their consorts. All of them enjoy popularity, bigger than in their days as heirs. It is impossible to tell if the British will like King Charles and Queen Camilla. I think there is every chance that they will like them indeed.
No one of us has a crystal ball but I think when the Nation rallies around the King whom leads the mourning and then so many accents will change at the Court, the King and Queen are able to become dear to the Britons. Who knows. Since Victoria all Kings and Queens enjoyed popularity. Their Consorts likewise. Even Edward VIII enjoyed huge popularity until the abdication. We will see.