i somewhat agree with the idea all jadebloods have the potential for the mutation, but it does seem liek death has some relationship to manifesting the mutation in its complete form, since Doc Scratch and Aradia both highlight Kanaya's death as being the trigger for her drinkerhood

It’s possible for any number of things to have multiple triggers. Kanaya becoming a rainbow drinker when she died is important because it fits with Homestuck’s overarching death-and-rebirth theme, but just because it’s important by no means makes it the only way.