Does biofuel production by microalgae need an extra source of CO₂?
Maybe this is easiest understood comparing to our current rate of CO2 consumption to the possible industrial CO2 absorption rate. 

Human non biological CO2 production is 29 Gtons.  A little more than four tons of carbon per human being each year.  The natural carbon cycle on the planet through CO2 is otherwise about 788 Gtons.  



Is it possible to grow enough algae to balance our current rate of industrial production? I think so - it would be an additional 2% of the current carbon cycle.  In a first pass, that implies turning 2% of the non-productive earth surface into an average patch of ocean or forest/jungle.  

This is possible, but it would be expensive.  we're talking about flooding a desert basin for algae production. (numbers are from google). 

2% * (area of earth surface = 197million miles^2) = 3.9 M miles^2.  

Sounds doable, but remember that 70% of the earth's surface is already water and producing algae at a pretty good clip.  We'd be using ~6% of all the land for the algae farm:

For comparison,  3.9M miles^2 is larger than the continent of Australia.  (2.97 Million miles ^2), and bigger than the Sahara desert (3.6 M miles^2).  

just to get into the questions raised in the comments.... To DEPLETE the CO2 level in the atmosphere, we'd have to produce more fuel from the algae than we use - which seems to be impractical from a market standpoint - the fuel would be sitting around in warehouses while the plants die.  I can't imagine anyone making any money from this, and it would be expensive... so it'd be a strange set of circumstances that would deplete the atmosphere from carbon dioxide.  Also more oxygen probably would encourage more combustion and more animals too... so hard to see this happening.