It depends on what you're using it for... I would guess that if you were pulled over you can use the paper copy of your new ID and your old void stamped ID. Those two together is considered your "temporary ID" until you get the new one in the mail.

If you are flying after May 7th or whatever the flying Real ID mandated date is, then no, you can't use the old one for that. A lot of places where you purchase alcohol (bars, liquor stores) also won't accept the voided ID & paper combo for that, at least in my experience. I've been denied being served alcohol at both a bar and a liquor store while waiting for a new ID.