Yes you can eat sweet potato skin and it's very nutritious.
The skin of sweet potatoes contain the most nutrients of the potatoes so by removing the sweet potato skin you remove a lot of the vitamins and nutrients.
I love eating sweet potatoes with the skin on them.
I also love to peel the sweet potato skin and then deep fry the sweet potato skin and make sweet potato skin fries which are also good to eat.
Sweet potato fries are also good in the deep fryer but the sweet potato skins are also good to eat.
Eating the sweet potato skin will add even more nutrition to your plate such as fiber and potassium so you'll improve your health when eating the skin of the sweet potato.