Can't say for CI as they don't ship to the GWN but all other vendors I've dealt with gave me the impression they would solve such a matter fast and to my satisfaction. I've never had that specific problem but did depend on CS to resolve other issues without a glitch.
As far as "leaving them in the humidor for the same amount of time it took to get them" that, is a strange proposition at the very least.
How they were kept prior to being shipped (RH and Temp), how did they travel (Plane with Drastic Temp, RH and pressure changes or a truck with whatever it is outside that day) are all things that will affect the state of the cigar when you get it. So it's pretty much impossible to say exactly how many days it takes to stabilize a cigar in a given environment. One thing is certain, a day or four won't change much for a cigar, better leave it at least a couple of weeks for it to get to where it should be, where you like your cigars to be.
Although I sometimes fail, I do try to keep new cigars in there for months before I even think of smoking them. The bigger my stash, the easier that gets. After a while, there is always something you haven't tried other than the stuff coming ROTT so it's easy to fall back on something just as new and exciting but that you know for sure is right how you like it.
Just my $0.02.... about $10 worth of it