I doubt it. Unless you are using inferior chemicals, salts like KNO3 and K2SO4 should completely dissolve.
For this method, it doesn't matter if they cake or clump. There is a concentration gradient between the saturated solution in the vial, and the water outside it. Controlled by the valve, the heavier saturated solution moves down, the water moves up into the vial.
Nothing clogs. If salt crystals are blocking the valve, they dissolve the fastest. If that seems like an issue, you can use a bit of sponge to keep the undissolved fertilizer away from the valve. I tried it both ways, with and without sponge, and don't see much difference in the solution rate. Without the sponge, you can cram a little more fertilizer into the tube = advantage.
When filling the tube, I first put in a little bit of water, then the salt, then fill it up with water, then stir it to make sure there is no air in it. The salt settles to the bottom, then I close the tube with the stopper/valve/syringe whatever I use, making sure there is no air in the valve which would block the whole flow.
It's really much easier than I make it sound.