Boiling a water with high temporary hardness does drop out calcium carbonate from the water when properly performed. So the calcium level of the water will be reduced by the boiling treatment. You can read about the process and its effect on calcium level in this article:
Decarbonation by Boiling
In that article, I provide a way to estimate the calcium reduction due to the decarbonation of the water.
Carbon filtering does not affect any mineral concentrations we are concerned with in brewing. It removes halogens and volatile organic compounds.
If alkalinity is the only problem, then acidification might be a good alternative for brewing lighter colored beers. Bru'n Water has the calculator for that.