No, you cannot. An expired driver’s license is legally not an ID anymore because it has expired.
If I had it my way there would be a 14 day grace period after a license expiring and it not being accepted at liquor stores. I just turned 21 and my license expired on my birthday, I have to wait 2 weeks for my new one to get here before I can Buy passports and id cards from travel documents agency online anything from a liquor store.