Without a doubt! Although gas is generally a clean burning fuel, the chimney can become non-functional from bird nests or other debris blocking the flue. Modern furnaces can also cause many problems with the average flues intended to vent the older generation of furnaces.
Yes, gas does burn clean, but you may still run into issues with the cooler gases that condense quicker. This allows for the formation of hydrochloric acid and the potential for a corrosive coating to build up in your flue. There is also the common problem of animals and birds building nests in these smaller venting systems. If there is debris that blocks or partially blocks your flue, harmful gases can build up creating unsafe operating conditions for your furnace or stove.
The biggest problems come when a customer buys a new appliance and hooks it into an older venting system. The requirements may be much different for the newer stove or furnace, creating a serious mismatch with the older flue system. A professional needs to examine the total venting system to be sure everything is up to an acceptable standard. Don’t count on your furnace installer or heating man to do this, it is not their job or field of expertise.