1911greg,
You can transport an unloaded shotgun in your truck. I also think it's o.k. to have a box of shells in the glove box at the same time.
Here is the definition of "loaded" from Penal Code 12031(g):
"A firearm shall be deemed to be loaded...when there is an unexpended cartridge or shell, consisting of a case that holds a charge of powder and a bullet or shot, in, or attached in any manner to, the firearm, including, but not limited to, in the firing chamber, magazine, or clip thereof attached to the firearm...."
In [u]People v. Clark[/u] (1996) 45 Cal.App.4th 1147, the court of appeal in San Diego discussed PC 12031(g) and said that a single-shot shotgun with "three shells located in a covered compartment at the rear of the shotgun's stock" was [u]not[/u] loaded within the meaning of that section. (There was no shell in the chamber.)
Although this was not the technical holding of the case, it's the best case I know of that discusses PC 12031(g). You can get the opinion at www.findlaw.com.
I'm not sure that I would come right out and tell a cop that pulled me over that I had the shotgun in the vehicle. If you do, the stop is definitely going to get more complicated. If the cop sees the shotgun, the stop is going to get complicated anyway, but why volunteer the information if there's a chance the cop isn't going to see it?
What I would do is put the shotgun in some type of bag or case that doesn't look like it was made for a gun, and if any questions come up, just politely decline to answer. I would also keep my registration and proof of insurance in some type of clip-on visor pouch, away from the glove compartment where you keep the box of shells so you don't have to open it if you are pulled over.
There's an interesting case from the 10th Circuit Court of Appeals on whether a cop can inquire about guns in the vehicle and other vehicle search issues: U.S. v. Holt (D.C. No. 99-CR-77-B). You can download it from the 10th Circuit web page. If you're carrying a gun under your seat it's worth a read.
Hope this helps,
Ed