We don’t give advice, but if we did, we’d advise against using non-dairy creamer in huge quantities and on a regular basis. Most are pretty chock-full of chemicals and additives, and based on coconut oil, palm oil, or other hydrogenated oils. Most of the half-dozen or so dairy-avoiding cookbooks that we looked at to help answer your question either trembled visibly at the thought of using non-dairy creamer in recipes or avoided mentioning it entirely. They want you to lean toward soy milks, rice milks, and almond milks.
the same time, we know people who have used non-dairy creamer as a substitute for milk in pumpkin pies and other high-flavor dishes (where the taste difference between milk and the creamer is less noticeable), and they are still walking the earth.
Corn starch or other starches cause a pudding to thicken, and we are not aware of any ingredient in a creamer that would defeat this, but we did read something somewhere about non-dairy creamers hampering the thickening of instant puddings.
One upscale brand of non-dairy creamer, International Delight, (which comes in a wide variety of flavors, including Irish Creme, Amaretto, Cinnamon Hazelnut, Chocolate, Kahlua, Southern Butter Pecan, etc., etc.) suggests that not only can you use it in cooking, you can drink it straight over ice “as a delightful non-alcoholic drink.”. The company provides a number of recipes on its web site. We’d read the ingredients’ label first, but perhaps it might be useful in making ice cream.