You only need to wait if you're turning in tags early for any reason, so you can get a receipt.
Good question. The last time I did it I believe the answer is no. But if you want to get any kind of receipt for it, you would have to wait. My suggestion would be turn it in and don't wait if you can't. This location moves pretty quickly. Check back with the DMV a few weeks later and make sure they got the plate.
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