You have a basic misunderstanding of how salts work in solution.
When you dissolve MgCl2 in water, the Mg2+ and Cl- ions part ways. In solution there is no such thing as MgCl2. It dissolves. There are Mg2+ ions and there are Cl- ions and they are all surrounded by water and spread out and really don't interact much anymore. If you were to evaporate salt water and crystalize all of the salt, you still wouldn't find MgCl2. The magnesium will come out with hydroxide and carbonate, because Mg(OH)2 and MgCO3 are much less soluble than MgCl2. So they will precipitate at a Mg2+ concentration where MgCl2 is still soluble.
That solubility thing is the reason we use MgCl2 to dose back the magnesium. And why we use CaCl2 to dose calcium. You can put a lot more magnesium in the same amount of water because MgCl2 is way more soluble than MgO or MgCO3, especially at pH higher than 7.
The concentration of chloride ion in your salt water is so much higher than the amount that you are adding when you dose with MgCl2 that the added chloride really has little effect. In
Randy's DIY 2-part article there is a discussion of using epsom salts as a less expensive source of magnesium. In it there is discussion of the relative concentrations of sulfate and chloride and the proper balance to maintain.
So the take home message is this. It doesn't matter what two ions you add together, so long as you realize you are adding both. Adding MgCl2 and Na2CO3, is equivalent to adding MgCO3 and NaCl. Except that you would need low pH to dissolve the MgCO3.
