Yes, calcium does alkalize your system. But a calcium supplement that as an isolated nutrient is completely foreign to the body. Isolated nutrients can cause nutrient imbalances, congested liver/gb, kidney stones/congestion, etc.
Best to take a whole food supplement, like a green food supplement as I mentioned before, which will give you lots of calcium in addition to an array of other nutrients and help alkalize your system. Whole food supplements are always a better choice than isolated nutrients.
More an more studies are coming out showing that isolated nutrients (i.e. vitamin supplements) can often times cause more harm than good. Whole food supplements are the way to go when supplementing your diet.