I think anaerobic bacteria probably starts to thrive in the botom of 3 inches of sand...
So ya, for a deep sand bed 4 inches is great. Remember, though, aragonite sand does dissolve over time, so you'll have to add sand as the years go by.
Also, for a deep sand bed to function properly to need to make sure you have plenty of micro critters in it, brisk current, strong skimming, no "dead" zones in current, no sand "sifters", etc.