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No they won't. Metal corrosion is caused primarily by acidic conditions (low pH), not by a low calcite saturation index. A technical discussion about this is in this link. When you are using bleach, the pH will tend to rise so a lower TA helps prevent that since TA is a source of rising pH from carbon dioxide outgassing. When you are using Dichlor it will lower TA so be careful. You may need to add more baking soda to maintain the TA. For every 10 ppm FC added by Dichlor, it will lower TA by 3.5 ppm when the chlorine is used/consumed.
The lack of calcium carbonate saturation of the water is bad for plaster/gunite/grout surfaces because it will tend to dissolve the calcium carbonate from those surfaces.Dissolving of plaster and corrosion of metal are two completely different things. The theory that saturating the water with calcium carbonate will prevent metal corrosion is not practical nor consistent. The idea is that you coat the metal with a thin layer of calcium carbonate scale, but that is very hard to do in a spa when the water is not always flowing through the pipes (i.e. the pump is on and off) and the temperature is varying a lot (i.e. the gas heater goes on and off). It's much worse to saturate the water, fire up the heater, and get scale in the heater that builds up as that will lower heat conductivity and burn out the heater.Tap water is typically very soft yet it isn't corroding the copper pipes in your house. My tap water only 55 ppm Calcium Hardness (CH), 80 ppm Total Alkalinity (TA), a pH of 7.7, and a temperature of 67ºF so has a saturation index of around -0.7 which should be "corrosive" according to pool and spa industry lore. It isn't. The water company does add 300-500 ppb orthophosphate to reduce corrosion, but the soft water itself is not "corrosive". Metal corrosion comes from oxidizers in the water such as dissolved oxygen and chlorine, but is mostly affected by low pH. Keeping the pH from falling is the best way to prevent metal corrosion. This is because metal such as copper, aluminum, and stainless steel all form oxide passivity layers (coatings) that inhibit further corrosion. Low pH is most disruptive to these coatings, except that high chloride levels can interfere with stainless steel's passivity layer especially when sulfates are present but that's more of an issue in saltwater chlorine generator pools than in spas (even saltwater chlorine generator spas tend to use lower salt levels around 2000 ppm compared to 3000 ppm in pools).In order to reduce foaming, one would normally have 120-150 ppm CH anyway and in this particular poster's example of his water, the calcite saturation index is only -0.3 at 90ºF so not that low anyway and when the water is 104ºF, in the gas heater when on the temperature at the heat exchanger is around 134ºF so the saturation index would be around 0.0.So focus more on making sure the pH doesn't drop too much. This is one of the reasons that Trichlor pucks aren't usually used in spas. It's not just that they dissolve too quickly, since that could be addressed with special feeders, but rather that it's too easy to overdose and have the pH drop too much in the spa and that then causes significant damage. Even Dichlor is net acidic and will use up TA, but at half the rate of Trichlor so tends to be safer. Also, Dichlor's net acidity (when accounting for chlorine usage/consumption) helps balance the pH rise from carbon dioxide outgassing. Again, focus on pH and not letting it get too low.Of course, there are manufacturer's warrantees to consider so you might as well add calcium to cover that and to reduce foaming anyway. As for other levels like TA, you can't follow the manufacturer's typical 80+ ppm recommendation for that and have stable pH when using bleach or even sometimes Dichlor if you've got lots of aeration. So that's a conundrum. Do what's right chemically or follow the manufacturer's recommendation to not void the warrantee.