Coconut Milk Bread Pudding

An excess of coconut milk and a desire for cinnamon rolls collided recently in the form of this bread pudding, made from a modified "New Orleans Style Bread Pudding" JOY recipe (1 cup of sugar instead of 2, coconut milk instead of regular milk, and no bourbon sauce!)

The coconut milk I'm referring to is not the kind that comes in a can--this is a new product from So Delicious that has appeared at the grocery store recently, and that is being marketed as yet another milk substitute (along with soy, almond, hemp, etc.).

My question: can it be used in baking, and if so, will it leave evidence of its pleasingly faint coconutty flavor?

The bread pudding turned out fine, but lacked the coconut flavor. However, warming it with a little coconut milk poured over the top did the trick.