Yes.
They're on the flat side - black or a blue-black in the ones I've seen, and I've seen a couple of shelving units' worth of them - the damndest accumulation of first generation Colts you'd ever want to see.
Most original boxes don't survive well - that accounts for the truly serious prices on originals.
For that matter - most Colt boxes.
Cardboard of the time frame wasn't designed to last and last, like that of today - and the paper had a high sulphur level that caused its deterioration while you were looking at it.
Firearms of the era were designed to be used, too - so most boxes were discarded in favor of holsters.
If you see 'any' period revolver with its little cardboard box - Colt boxes looked like that.
Vaya,
Scouts Out!