The question in the original post is an interesting one, from an analytical point of view. The answer is fundamentally the product of two other questions: (1) How precisely can I measure analyte X? and (2) How much of analyte X can I add without adversely affecting the health of my tank's inhabitants?
You need to be able to take your tank from some relatively low value of some analyte you can measure, and then dose a relatively large amount of that analyte all at once. You need to also be able to test immediately before the dosing, and also long enough after the dosing for the dose to have reached equilibrium with the rest of the tank water. You also need to be able to measure the absolute amount of the analyte added during the dose.
One considerable limiting factor is the difference between the lowest recommended and highest recommended amounts of the analyte. It's not as though you can take Magnesium, for example, from 0 PPM to 1500 PPM at once; you will more likely be taking it from 1100 PPM to 1500 PPM, or something like that. Even if you can measure (in this example) Mg to +/- 15 PPM, and your method uncertainty for the Mg test is along the lines of 15 PPM / 1380 PPM = 1.1%, your relative precision for measuring the difference before-and-after is closer to 30 PPM (2 * 15 PPM) / 400 PPM (the difference between 1500 PPM and 1100 PPM) = 7.5%. Add to this the uncertainty in the actual amount of the analyte dosed, which could be from 1 to 5%, then the uncertainty in the estimated tank volume is likely around 10% or so.
So, if you are comfortable using this technique to say that your tank volume is, for example, 100 gallons +/- 10 gallons, then it just might work for you, if you pay careful attention to each detail of the process.
That said, I have used this exact technique, together with a Total Hardness (Mg + Ca + Sr) method with a precision of around 0.25%, and the ability to measure the concentration of MgCl2 to within 0.1%, to estimate my total tank volume to be 201 gallons +/- 5 gallons. With precise methods, this technique can be used to accomplish your goal, within reason, but it does require more equipment and dedication to consistent methods than most hobbyists are willing to commit to.
