It's possible, but would require some more context as the obvious question would be 'What are you?' The shortest sentence in English would consist of a single imperative. 'Go!' would probably be the shortest as I cannot think of a single letter imperative, but the imperative does not require a subject as it is understodd. ;-)
Technically not, because it is an ellipsis for I + verb, whereas an imperative requires no more context. 'I' would be a sentence fragnment or minor sentence. ;-))