I highly doubt that can be implement. Except, of course, on artifacts, where infinite regression seems to be a fact of life for most. More realistically...it would function like a hatch a dwarf can't drop through unless something-a spear, hammer, or barrel of Dwarven explosives booze comes and knocks them in. As a side note, they should immediately seek out a shower or tile of water deep enough to wash it off. Or be forced to by the fortress guard, if there is a risk of infection. Doctors might actually refuse to treat such dwarves until they wash off. Would also make it USEFUL to not mod in tamed fire imps, or to actively seek out fire creatures-they could be in the cistern to dispose of waste before it becomes problem. Alternately, lacking access to gas, they could simply take a barrel of booze and set it on fire. Better yet would be a bucket to poor said booze into, light it, and then use it like a match to dispose of accumulated waste. It would need to be retrieved afterwards of course. Alternately, yet another use for burning coal besides draining oceans would be to serve the same purpose.
Giving several options for disposal would also be useful. To deter overuse of "poop trap" pits, they should automatically create a miasma if the waste accumulation grows too large (meaning its not a good idea to have that right in front of your door). Potentially detectable by dwarves passing above the pit. Alternately, if smelling does deter gobbos/elves/humans from passing through it (kind of how "restricted paths" works for dwarves), it can be used to "funnel" enemies. And if disease is implemented for it, it could also be used to infect a besieging army and weaken them. Forcing them either to loose soldiers or to have doctors and personnel who treat the diseases and try and get rid of the waste. Would be useful if, in response to a locked doors response to siege, the enemy poisons your water supply. You have a way to counterattack while you attempt to prepare your military.
The economic aspect is also realistic. If you think about it, the viability of potash as a fertilizer is limited to the availability of trees. If you're in the middle of a forest, that's fine and dandy. However, if you're not, you'll need to find another source of fertilizer. This is where the fertilizer aspect would come in. By affording an easy source of fertilizer, it would be possible to reserve your wood for more useful stuff-like smelting if magma is not available, and carpentry, ballistas, and of course crossbows early on (which, incidentally, would free up metal if you were making copper or other metal crossbows). This in turn would mean you might not need to trade for as much wood, or can make better use of what you have. At the same time, it should have the drawback of the plants gown like this needing to be "cleaned" before consumption (which, incidentally, is what we do. There are restrictions, in the U.S. at least, on the use of human fecal material as fertilizer, and i believe it must be cleaned very thoroughly due to the potential presence of disease causing agents for humans in the fetilizer). Animal manure might work far better for this though, and was used by peoples such as the plains indians as a fuel for fire. Besides, having "stables" to limit manure spread would also come in handy if/when dwarven war mounts are implement (I'm thinking war bears or boars, since they seem especially dwarfy).
Will add more later.