In my personal, non-lawyer opinion, if you're not in the vehicle then I don't see how you'd be "carrying" it "upon or about" your person.
Here's Delaware's law against carrying concealed deadly weapons:
11 Del. C. §1442 Carrying a concealed deadly weapon; class G felony; class D felony.
A person is guilty of carrying a concealed deadly weapon when the person carries concealed a deadly weapon upon or about the person without a license to do so as provided by § 1441 of this title.
If it's in a lockbox in a locked vehicle then that would seem to further decrease your "immediate availability and accessibility of the weapon," which is what determines if the weapon is "about" your person according to a court case (excerpts of which can be found in our Firearms Law pdf that KuntryBoy linked to):
Whether concealed deadly weapon may be deemed to be "about" the person should be determined by considering the immediate availability and accessibility of the weapon to the person, which is a factual question. Dubin v. State, 397 A.2d 132 (Del. 1979).
Factors determinative of accessibility. - Three factors are to be considered by the fact-finder in deciding the issue of whether a deadly weapon was accessible to the defendant and, hence, "about the person": (1) Would the defendant have to appreciably change position in order to reach the weapon? (2) could the defendant reach the weapon while driving? and (3) how long would it take for a defendant to reach the weapon, if the defendant were provoked? Dubin v. State, 397 A.2d 132 (Del. 1979).
1. You'd have to return to your vehicle, unlock your vehicle, get into the vehicle, unlock the lockbox, and then retrieve the firearm. Personally I'd say that's an "appreciable" change in position.
2. You're not even in the vehicle, so no you can't just reach it.
3. Seeing the steps needed in #1, performing those steps would take significantly more time than say pulling a gun out of your waistband.
Of course, when you get back to the vehicle, if you don't have a CCDW then you need to either move the firearm into the open (to OC) or make sure it's someplace that isn't accessible to the occupants (perhaps the trunk).
Furthermore, whether or not the firearm is loaded is "immaterial"
It is quite immaterial whether a revolver is loaded or not, because such an instrument is commonly regarded as a deadly weapon without regard to its condition. If the absence of bullets would make the weapon a harmless one, then any condition that would prevent its being used at the time injuriously would have a like effect. State v. Quail, 28 Del. 310, 92 A. 859 (1914).
Since it's immaterial (atleast in regards to the CCDW law) I just leave mine loaded while it's secured in my vehicle (on the very, very few occasions where that happens).