If renewing by mail, you MUST send it in with the renewal application. If you are renewing in person, it seems you don't need to. It states the reasons why you MUST submit an application in person, listing a lost or damaged passport as one reason, but I never saw anything that required you turn it in if you were renewing in person. I think the only concern would be at what point is the passport in hand cancelled - if the passport renewal was processed just before you leave and shipped to you, could the old one no longer be valid? That would be the only concern. I'd confirm all of this, this is just what I noticed when looking at our last renewal.