That will vary between tattooer and shops. Some charge a drawing fee and others don't. Often a drawing fee is a way of keeping them from wasting time on a drawing and then having the client bail out.
Edit: I saw you were thinking about a tree. Trees are really cool and work well as tattoos in most cases. I wanted to give you a heads up, that depending on the style of tree, some tattooers may prefer to draw it on your skin so that it fits the form of your body properly. Be open to that idea.