I strongly agree with using a peristaltic or other precise dosing pump on a timer or other failsafe of somesort.
True you can rig up a kalk drip connected to a good ATO system and it will work great. Problem is, if you lose or remove some water the ATO will fairly quickly replace it with kalk. That could be really bad if, say, your skimmer overflows a gallon, or you bag a bunch of frags, or some sort of leak happens.
By using a dosing pump on a timer you can deliver a consistent measured dose of kalk and not have to worry about an overdose due to lost water.
By using a dosing pump on a timer, then connecting that to a good ATO, you can get a very consistent drip matched to your evaporation rate, AND have a failsafe (becuase the timer can be set so that even if the ATO stuck "on", the amount of kalk drip in a 24 hour period would be limited). The timer would limit you to dosing the kalk in 5 or so spurts per day, but that should space it out enough that it would minimize any PH spikes enought to not have a problem.
Personally, I run a cole-parmer peristaltic pump on a timer so that it drips about 80-90% of my evaporation during the night (something like 64oz in 10 or so hours). This is the kalk drip. A simple mechanical float valve to gravity feed of RODI makes up the difference. This way there is no way the kalk can overdose, and if I remove or lose some saltwater from the tank, the RODI will water things down a bit, but the kalk won't cause instant disaster.
As to the original question - "what does kalk cover?"
Kalk adds Ca directly, and supplements alk indirectly by neutralizing acids that would otherwise deplete alk. It acts as a "balanced additive" meaning that it should maintain both levels in balance. Kalk doesn't add anything else important, though it is sometimes said that it depletes Mg. Kalk does not deplete Mg, but Mg is used up in calcification with Ca and alk, so sometimes you will see a decline in Mg when a tank is primarily maintained with kalk (because all 3 are used up together, but kalk only maintains 2).