Submiting I9 should not hurt you in any way
All it has is your GC info like your A number, which your employer can get anyways if they wanted to. Gov. regulation requires the company to maintain this info, so if they haven\'t already asked you for it, I\'m pretty sure they will. As an employee, it is also considered to be your duty to inform your company about any changes in your visa status. But ofcourse it is not mandatory. Just that it may count against you in case of problems.
Can the employer do any harm here after ? Unfortunately yes. In the sense that they can inform INS that you abused the employment based GC as you falsely claimed you wanted to work for the company. The onus will then be on you to show why you left and that you had every intention of working for the company at the time you got your GC. A rough guideline beyond which such a claim would be rather rediculous by the employer would be about a year. Usually companies don\'t venture into all that since they have nothing much to gain from it (unless ofcourse they go in with some civil case that it caused them some heavy losses).