Your thread on the Physics Forum was closed before I had a chance to respond and I am sorry that your exchange posts took a turn that was of no real benefit to you, so here is my feedback on your proposed system; and, I am willing to discuss its elements at more length if you so desire as well.
From my view, it is not a matter of "will it work", it is more a matter of "is this an efficient or more efficient way of converting the energy of waste gas and matter to an output form of energy i.e. electricity".
Viewing your diagram, basically each element will work but with a limited degree of performance and one main feature, water to steam to water circulation cycle is of no benefit. If the water tank and fired tube are viewed as a closed system, the water in the tank will circulate through the tube and be heated to steam as you propose due to the fact that the water column in the tank is denser than the steam in the heating tube; however, because keeping the output steam turbine running requires a constant outflow of steam from the system and therefore a constant inflow of water into the system, the water stored in the tank serves no real purpose. It is more efficient to simply feed the incoming water through a preheating section (as you have done) and then directly into the fire box tube and then directly to the steam turbine.
As discussed in the other thread, it is the steam pressure that provides the flow that drives the steam turbine and converting the energy from the waste burning to steam is simply a method of converting that energy to a form of energy (steam) that can used to turn the turbine and the higher the combined heat and pressure energy in the steam the more energy there is to drive the turbine.
Using the feed water system you show without a water supply pump means that the maximum amount of pressure you can maintain in your tank is only equal to the water head in the short feed tube you show in blue in the left upper corner of the diagram because if the pressure in the tank exceeds the weight of that short column then the tank pressure simply push the water back into the box; and 2 psi of pressure no matter how hot the gas (steam) from a 4 ft water column is simply not going turn a steam turbine.
Apart from those issues, yes, each the mechanical elements shown in your diagram will function, but taken as a complete system the unit there is no breakthrough element in the design that will allow it to generate an energy output (electricity) at any better efficiency than the direct water to steam to turbine systems now in operation using waste gas and matter as a boiler feedstock.