My wife likes salt cod-she prepares it in a variety of ways. The stuff looks like hard plastic-it is dried by immersing it in salt-which removes all traces of moisture. The salt also inhibits bacteria. Basically, salted cod is like an Egyptian mummy.
Can it remain edible for centuries?
I doubt centuries but a large number of years is certainly possible if it is stored correctly.
I consider the stuff the RoundWorld equivalent of dwarf bread. 
Fats will oxidise and turn rancid, proteins will denature on exposure to light and trace amounts of ozone etc - I think this will result in the surface of the preserved food crumbling away minutely over time.
If you were to vacuum pack it in thick, impermeable plastic and store in a cool, dark place, the storage life will be considerably extended - maybe remaining edible for centuries, for certain values of ‘edible’.
I started reading DiskWorld books a few months ago. So I get it! ha ha!
According to this page, canned food can remain edible for over a century, albeit not as tasty or nutritious after that time; for shorter periods of up to several decades, food has been found to still appear fresh and retain nutrients (as an aside, while nutrients are lost during canning, nutrient levels of canned vegetables are similar to cooked fresh vegetables because nutrients are lost really fast; frozen vegetables can be more nutritious than either due to being picked when ripe and little nutrient loss when frozen).