I've had used hard rock, clumped and rock solid salt before, IO salt, I've mixed it slowly and I've throw big chunks in the mixing container, in both ways the calcium in it precipitated , and didn't mixed well, I ended with a thick coat of powder in the bottom of the container everytime I've turned the mixing pump off. It won't mix well as it were a brand new batch, I had the pump and heater in the container to have a better reading on it.
I would say yes, Alk could drop by certain degrees due to precipitation. What I did trying to compensate that was add a two part supplement, however, I can't assure my alk was where it had to be since my testing pack was some of the cheapest.