Can you use a round shader to do outline on your tattoo?

If you were to be doing a portrait which would have fairly blurry lines without really sharp depth, then perhaps. But in most instances, this would not be the ideal needle choice for the job. You would want to use a needle suited specifically for outlining where the needles are concentrated in such a way that they come together to produce a nice clean line as opposed to the circular configuration of a Round Shader which is made so to give you the nice rounded appearance when grouped up appropriately for something that requires blending and nice solid work in small areas. So in a way, yes you can. The smaller the Round grouping the better though, as having anything above say a 10RS would be a bit too big to manage easily.