Adding Bicarbonate with Sparkling Mineral Water

Let's just take it as a given that I want to increase the bicarbonate in my beer. The particular beer I'm working on is an extract porter and my tap water has very little alkalinity. I want a moderate level of alkalinity to soften the acridity of the dark roasted grains a bit. But again, let's just ignore those details and assume I want more alkalinity in the kettle than my water would otherwise provide. (And yes, I know the DME itself will provide some minerals. Let's assume it doesn't provide as much alkalinity as I want.) What's unique about my situation is that I don't need the chalk to be dissolved in the water for the mash, because there is no mash. I just want the final beer to have some alkalinity because by many accounts that makes for a tastier porter.

So to start, I could always add baking soda (sodium bicarbonate). The downside is that this would elevate the sodium in the beer, which I don't want to do.

Chalk (calcium carbonate) is another potential source of carbonate. I think these days everyone knows that chalk dissolves poorly in water. That's maybe a bit less true at the pH my wort will reach in the kettle (I'm thinking low 5's), but still I'd like to make sure the carbonate gets into solution.

One technique that homebrewers have used is dissolving chalk in carbonated water. The carbonic acid in the water helps dissolve chalk. Here's an explanation from Kai Troester:

http://braukaiser.com/wiki/index.php/Building_brewing_water_with_dissolved_chalk

Now my question is... assuming the other minerals in the water are acceptable to me, is there any reason I can't just buy a couple of bottles of carbonated mineral water that contains the carbonate I want and add them to the wort? The brand I have in mind is Gerolsteiner (the carbonated version, not the still one), which contains a truly ludicrous amount of bicarbonate. Adding 1 or 2 liters to my 5-gallons (6 gallons in the kettle) beer should provide all the bicarbonate I need. And actually I don't mind a little extra calcium, magnesium, etc., which the Gerolsteiner will provide.

As an aside, since Gerolsteiner is a drinking water I'm pretty sure it's Reinheitsgebot compliant, but this is of no importance to me. I mention it only for those who might be interested.

Any thoughts? As I add the mineral water to the wort in the kettle the carbonation should degas almost immediately. So there's some chance a portion of the calcium carbonate will come out of solution. However, as mentioned before, the pH of the wort should be favorable for keeping the calcium carbonate dissolved.

As a final point, I suppose I could add the chalk to the fermenter. As the yeast generate carbon dioxide, a portion should remain in the beer as carbonic acid, creating a favorable environment for dissolving the chalk. So maybe I've overthought this.