The manufacturer of Gun Juice does not recommend against the use of the product for application for storage of a 'cleaned' bore. [In fact the manufacturer recommends the product for application for gun storage purposes too. Of course.. they do sell Gun Juice.] I've never had a bore corrode in storage when stored within my home outside of a gun case, whether the bore was cleaned or not, other than when I've left ammonia based bore cleaner in the bore (don't do that). I suppose if you live in a high humidity - sea shore environment - then better safe than sorry and clean and oil coat your bores after every firing session. Where I live - I just leaved the bores fouled until I feel that a cleaning is necessary for accuracy, or until I believe the guns will be in storage for 6 months or so. During the hunting seasons I just leave them fouled in storage.
After you've treated a bore with Gun Juice, I rather doubt you need to worry about firing the first shot on an oiled bore. The bore has already been sealed and coated with a friction reducing agent. Certainly the benefit will be reduced for a Gun Juice treated bore compared to firing over a bone dry steel bore. For non-Gun Juice treated bores, Kirby's stored lightly oiled method to decrease first shot fouling certainly makes sense. I'm glad he covered that and I think it a good standard operating recommendation and practice.
Placing some oil in the Gun Juice treated bore for storage certainly won't hurt anything but I doubt there's any perceivable benefit. Hey, if it gives peace of mind, well then it's well worth the peace of mind. $0.02 for the wetted patch, oil, and peace of mind.
Tiger Woods would be thrilled with the cost-effectiveness, comparatively speaking.