Yes, it's correct, if the two clauses are connected properly.
As a native speaker, I think that it would be appropriate in a situation where someone asked if it was necessary to perform a specific task, and the response was that the person asked performed the task, and had the authority to command the asker to do so as well. This would be grammatical because the verb is implied by the question that had been asked.
For instance, this would be grammatical:
"Hey, boss, do we need to fill out the form this way?"
"I do, and so shall you."
In this case, the respondent would be saying that they do fill out the form that way, and are further stating that the asker will also fill out the form that way, or else they will face consequences if they fail to comply.
There would be a technical nitpick about the grammar, though; you should either include "and" after the comma, or replace it with a semicolon or period, so that the two clauses are properly connected.
"I do, and so shall you."
"I do. So shall you."
"I do; so shall you."