Do I always have to peel garlic?
I don't think that this would be unsafe, as you do see unpeeled garlic used in some applications, but it wouldn't be particularly pleasant and you probably wouldn't end up with a great paste. Garlic skins can be pretty tough and woody depending on the particular bulb; you'd probably end up with hard, fibrous bits in your paste.

If you're willing to accept this negative impact to the final texture, then I suppose you could try it. But as @Joe points out, you're better off working on an improved method of peeling your garlic, which will serve you well no matter what you're cooking.