Yes. Anyone who files a green application, either through marriage to a US citizen or any other grounds may request the USCIS a temporary work authorization, so he may legally work in the United States while his green card application is pending. You should file an application for employment authorization together with your green card application. Within normally 90 days from the date that you filed your green card application, the USCIS will send you an employment authorization card. The employment authorization card allows you to legally work in the United States until a decision on your green card application is made.
If your green card application is approved you no longer need to use the employment authorization card, since the green card provides you with the right to work in the US.
If your green card application is denied you may no longer use the work authorization even if has not yet expired.