Let's answer this question slowly: Do any Islamic dominated countries have a Starbucks?
Starbucks is a coffee shop found in numerous countries including USA, China, and the United Arab Emirates. The United Arab Emirates has a Starbucks in Dubai. Islam is the largest and the official state religion of the United Arab Emirates. Pew Research estimates state that over 76% of the citizens of the United Arab Emirates are Islamic. So the answer is yes.