m0useanswered grow question a year ago As long as they are getting mixed into the medium and its not to wet getting watter from the top down I don't see a huge problem.
If the autopot's only water from the bottom up it could be hard for it to dispense though out the medium when hey are fed by mixing into the top level of the substrate. Watering from the top pulls em down into the mix and helps the bits go deeper into the substrate to be broken down by microbes, the ones that are broken down and available already "waster soluble nutrients" gets pushed deeper into the root zone for absorption into the plants. This is why you normally don't water with run off on dry amendments as they leach out easily as you tend to only PH the water not add nutrients to it as well. so all runoff will contain the things the microbes already broke down.
The amending aspect is hard when there is no transplanting as dry amendments tend to need a top up every 3-4 weeks either from transplant or incorporation of more amendments into the top layer.
one other option would be to ferment the dry amendments in a nylon sack in the reservoir or someplace else with oxygenated water and some bacteria, maybe laco bacc. once the bacteria decompose it it will become available like hydro nutes, No idea how fast it is or the after affects of this but it could be an option. I do think this will clog up your tubes and pumps though as they are whole ingredient items not just salts so their will be leftovers that normal get trapped in the soil and become part of it. most amendments are ground into a fine power to increase surface area so they break down faster but this also means its easier to clog up things.
Auto pots might be best with hydro nutrients because of the things mentioned above. Again never tried it, but have grown with dry amendments in soil and that's my prediction and theory on how it could work. take from it what you will.
Good Luck!