Is it possible to install a bike rack on a Cessna 172?
Is it practically possible to do that? Is it okay in terms of
  weight, CG?


Bikes (depending on make and model) are not all that heavy and in this picture they are more or less center mass and would most likely fall in the CG range.


  aerodynamics


Again this depends on the bikes and the placement but with proper care you could be ok. Admittedly a bit different these bikes would create no more drag than say a wing walker would and people have been doing that for some time, 

 

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keep in mind bi-planes fly a bit slower than a 172. But on the small vehicle transit front the PBY-Catalina carried a full sized rowboat under its right wing for use when you arrived at your destination. Interestingly it seems to be mounted backwards which I would think is the non aerodynamic way to mount it...  



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It looks like at least one guy has actually managed to pull this off in New Zealand



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  In case you were wondering if it’s legal, the Civil Aviation Authority
  of New Zealand has approved the design.


And he used a Cessna 185. Important to note that these are mounted under the wing which keeps them out of the way of the rudder as Dan mentions but more importantly should anything go wrong the bike would shear away and fall down away from the aircraft instead of back into the rudder.

It looks like this kit plane also offers a similar rack.


  ....If it was possible, would there be any chance it gets certified for use?


In New Zealand yes, in the US under the FAA, depends how good you are at paperwork.