Is it possible to ask a question with just a single noun?
Sure it is, in oral Chinese, you can question someone if they care for tea like


  茶？


You do not need 吗 as the question marker.

When you use this expression, please make sure, first, both you and the person you are asking are in the same and easily understandable context, like, you holding a teapot and an empty cup in front of that person; second, the person you are asking had better be in a relatively equal standing with you, this is a very casual way of asking!