Hoovering off carbon dioxide, is it realistic?

First of all, I am an all out fan of the Carbon Capture and Storage technology. It has been already a few years I have been gathering information. As I love to dream and picture simple stuff in my mind (it kills time off metro-commuting for example) I always figured out a bright future, Brand-New-World lookalike with pastel colour automatic little hoovers buzzing around busy city centers sucking off CO2 from immediate atmosphere and shiting calcium carbonate bricks*... like rabbits. I never said it was clever thoughs but the idea was keeping me intertained for long enough. Another of my thoughts was, due to the GHG effect retaining sunlight's heat from evading the Earth, the high CO2 concentration is probably up there in high atmosphere and not down here. So I was also trying to figure out the same hoovers but mounted in drones hoovering the stratospheres.
This morning I checked my internet alerts and discovered that Virgin's Sir Richard Branson launched back in 2007 along with Al Gore a contest called the "Virgin Earth Challenge". One of the challenger company made a news statement earlier this month regarding a pilot plant talking about... sucking off CO2 from atmosphere! So first I thought "niiiice", but then I remembered my drones and I wondered if it is not more efficient to suck CO2 off from high up rather than from the ground level? On the other hand, to give them justice, I know that some industries use CO2 as soldering atmosphere to avoid presence of oxygen around the flame and not having to use rare gas, much more expensive. This would mean that CO2 is heavier than air, hence would stay at ground level. That question I will leave it to further investigation, as it triggered my curiosity but for now you can watch this company's announcing video:

*: Calcium carbonate is a by-product of heated up and compressed CO2 in the presence of calcium which could be stored on a little batch reactor behind the hoover powered by sunlight. I had it all figured out, you see? :-)