Which of the following is correct?
1. The Hyderabadi departed without scoring, as did Gilchrist and Gibbs.
2. The Hyderabadi departed without scoring, so did Gilchrist and Gibbs.
When do we use as/so?
The first is correct.
The second requires a semi-colon or a full stop between the two complete sentences (that is, before the word "so"). The error here (run on sentences with a comma) is called a "comma splice."