Not a Pro in this field but I believe once you apply for the greencard you are in a whole new catagory when it comes to your visa status. You will be considered a "pending I 485" for your visa status and can stay legally in the country without a visa until you hear a decision from the USCIS regarding your greencard application. You can also work during this time if you have the EAD card.

Again, this is not from a person in this field.... but I am in a similar situation (expired H1 visa) but I am legally staying and working in the US with on a "pending I 485" status.