Un-identified

Is it possible to be completely un-indentified? Would there be advantages to this? Drawbacks?

Here's the thing. I do not believe it would be possible for someone to be un-indetified. This is because even if the individual themselves was somehow completely unable to find any sort of tie to any people whatsoever, outside forces would impose an identity on them. Be it a familiar image from the media, or existing radicalizations associated with said person, they would be identified as something by others.
Without an identity, people can not feel truly whole, but instead are floating between groups. Identities are crucial and necessary to being a person, in my opinion.

In Dick's Shoes

Theoretical situation: I am in Dick shoes, from the show "3rd Rock from the Sun", in the episode "Dick Like Me. I am completely unfamiliar with and unable to understand distinctions and divisions of race and ethnicity. How would I go about learning how to "perform"an ethnic identity?

I feel that I would go about it the way Dick did. I would read books about ethnicity and look at the pictures to see if there was a trend in the "title" of the ethnic group and the phenotypes, or facial characteristics of the people that belong to the ethnic group. Then, I suppose I would try and find people that look like me. If there were many different ethnic possibilities, or many people that I felt I looked a little bit like, I would ask people around me what they were, and ask them what they thought I was.

I don't know. It's a difficult question. I feel that any ethnicity I eventually chose to be a part of would be definition, be unnatural, and a form of self-ethnicization. Ethnicities have cultural aspects: food, dance, dress, etc. And they come with unique histories. To just decide to be part of one would mean forgoing the historical aspect of what makes an ethnicity and ethnicity, and therefor it would be very artificial.