No. The starter cultures require certain ingredients to be present in the medium.
They are:
- Fats and Proteins which determine the texture. For using with coconut “milk”, the milk needs to be made with shreds as they increase the fat and protein contents and deliver a thicker texture. Coconut water is a very light and processed version with a low amount of those, so the fermentation might not start. Additionally, if you buy those from the shop, you might find a lot of additives that certainly will kill any bacteria(all bad but also all good bacteria that are needed)
- Lactose or other sugar> sugar is the food that bacterial cultures eat
Please check this topic
You can use coconut milk when made with the shreds for a creamy texture, cashew and soy milk for a thick texture(with no additives and preservatives)