Not enough. My experience is:

You need I-485 and also EAD. If you were lucky, she/he might not ask for those documents. Same thing happened to me. But, if they asked, they will need see the EAD or H1B. They will give the valid drive license based on your expired date of EAD or H1B. So, don't volunteer your immigration documents. Renew DL year by year is terrible. It happend to my friend in NJ.
Good luck!