Yes you can but be moderate with your usage if you are just starting the Strike Phase.
Coconut milk has some carbs - which may vary by manufacturer. (as opposed to coconut oil which dos not)
See the nutrition label on the right. If you use a moderate amount it is probably acceptable.(To be absolutely sure you need to take some coconut milk and monitor what it does to your blood sugar.)
As an average a 100 ml portion of coconut milk can have 6 or more grams of carbs. Check the labels and remember the rule - be wary of any food that has more than 5 grams of carbs per portion.
Some members love the taste of coconut milk in their coffee.