No! But it does look yummy 🤤
Just be careful not to drink too much caffeine in a day
Whatever you can stomach is great. When/if the nausea hits there will be only very few things you can eat, so go for it.
Not the healthiest but no it won't hurt the baby in any way.
Be careful for the caffeine! I had a total of 4 cups of coffee spread throughout my pregnancy. They were like treats.