It does not matter if someone picks the gun up that you drop while logging out, you will still have the one in your inventory. We have done this 5 different times to be sure it was reproducible for the purposes of reporting it. The first time it happened we didn't think much of it and thought that the weapon in your hand just dropped, then down the road a ways my friend realized he still had the same gun in his inventory that I had just also picked up from the ground.
Edit: I'm not even sure if carrying 2 weapons like that at once is even intended. When you carry 2 weapons in that manner, every time you eat/drink/do anything that requires your hands the gun drops to the ground anyway (no dupe tho) and you have to pick it back up. If that is something not intended I guess we will have to stop carrying them like that when one of us dies, although it is useful for getting them geared back up a bit faster.