Two things tend to limit the possibility of over-extracting in cupping-style brews. First, as the grinds become saturated with water they sink to the bottom of the brewing vessel and pile up; if the water isn't stirred too much this slows any further extraction significantly. Second, the falling temperature of the brewing slurry also slows the rate of extraction, especially of the tannic components of coffee. The result should be a brew that highlights sweetness and acidity, with a moderate amount of body.
Folks who like to brew this way should keep an eye out for the soon-to-be-released Rattleware "cupping brewer," which lets you brew a cupping-style extraction and then put a plunger over the grounds so that you can pour out the brew without getting grinds in your cup. Conversely, this style probably works worst in an Espro or similar double-walled press-pot, given that such vessels will hold in heat for longer.