Someone asked about that very scenario. Wouldn't it put the officer at ease if you told him there's nothing in the vehicle? Made sense to me.
He said the opposite. He said it would stand out to him if someone led with "I don't have a gun in the vehicle." His opinion was he can see if you have a carry permit. If he sees that he approaches everyone the same regardless even if you tell him you don't have a gun in the vehicle. There a degree of unknown with every stop and somebody volunteering that information isn't going to make him instantly trust that they're being truthful. If he wants to know he'll ask.
Maybe he'd had an instance where someone lied. Can't remember.
I've heard a number of anecdotal statements where people were convinced they were let off with a warning in large part by handing over their CCW with their license/insurance and answering any firearm related questions. YMMV
