If I'm correct (hey, I don't know everything) these are partially true. Kalk does not increase your carbonate as much as that it increases you pH, which is an indirect way of increasing alkalinity as noted. It has limits in the reef aquarium though. The balance is related to the pKa graph here:
We don't really stray from that middle range in reef aquariums without killing things. Adding bicarbonate will drive you towards the middle of the graph. Adding OH- will drive you to the right, if the pH strays from the middle.
That being said, we have no idea what the OP's pH or calcium is, and there are numerous threads about not using kalk at high calcium, as is could drive precipitation of CaCO3. Thus hurting the goal of increasing CO3. CO2 itself affects pH, but not alkalinity. I've seen tanks with a KH of 5-6 with calcium over 900 (the reef version of "old tank syndrome"). I would never recommend kalk for such situations.
So here's what I did. I mixed a ton of kalk (I don't know, a few tablespoons? I dumped it) in a pitcher of RO water that had been sitting with air exposure for a week. Here are my test results after 1 hour:
pH is super high (8.8+) but the KH is <1. Perhaps this would increase over time with more CO2, but again I have gaps in my knowledge that others do not. The pH and alkalinity must both be high in order to convert CO2 into carbonate:
C02 Calculator
This calculator allows you to calculate CO2 Concentration. Simply enter water tempterature, pH, and total alkallinity and then press update.
pentairaes.com
If you raise the alkalinity you will find that your CO2 is actually higher than with lower levels due to the pKa. Perhaps I'm misunderstanding though (I welcome the opportunity to learn).
Here is what really set me down this path: a conversation with the chemist that developed SeaChem's products, who will not tell me a drop of information about ingredients (I'm paraphrasing it's been a year or 2).
Me: So I have a Seachem question for you.
My boss: Okay...
Me: I'm thinking of switching from Aqua Vitro Balance to soda ash. Do you anticipate any issues if I do so?
Boss: What are you trying to accomplish?
Me: I'd like to increase my alkalinity because it drops very quickly with all of my growth.
Boss: First of all, you're using the wrong product. Foundation is more of what you're looking for, and it's more-similar to what you're planning to use.
That's all I got out of him though. I welcome a more in-depth explanation if I'm wrong! I don't quite have it yet though. I've been using kalk for 10 years, but only in certain applications when I worked for an aquarium maintenance company and it was typically coupled with "here's some buffer (soda ash) add a spoon every week in your filter sock".
The real nugget of my posts is that you can get something 2x as strong as baking soda from your local grocery store. It made the difference between my tank making money and losing it. It's something I would never say in a LFS though, unless all of the customers were gone. LFS need those buffer sales!
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