It's doable, and is fine, as long as the DM is aware of how this will affect characters. In previous editions and in this edition, I've seen situations where PC either start out without equipment, or are captured and lose all their equipment. It's usually only temporary, there is usually a way to recover the equipment, and the encounters while you are running around without equipment will usually involve a degree of subterfuge, con work, or other chicanery. There may be a few fights, but you usually try to get surprise, wrestle an enemies weapon, etc. Armor can be an issue for a while, but even with armor, I've been in encounters where every single attack against me hit me. So running around without armor is not much different than running around with some bad luck for a while.
IMO, story always comes first. If the PC's are going to be without equipment for a short time, they can deal with it. If it will be an extended time, with many combat encounters, it may be wise to make some regional rule to cover the game mechanics portion. For instance if heavy armor is disallowed in a region, it may be wise to simply say those who normally wear heavy armor suffer -2 AC (rather than stripping the armor altogether) and their armor doesn't hinder their speed while in this region.
So, even "no equipment" does not necessarily have to mean no bonuses. A DM with a good grasp of the system can impose penalties to simulate various handicaps. 4e is quite flexible this way.