Burning natural gas in any appliance produces byproducts that can potentially be harmful to people. This is the basic way that combusting fuel works—after all, a fireplace can be dangerous if the smoke from the fire isn’t allowed to vent up the chimney and instead gets pushed into the home.
This is a way of saying that, yes, a gas furnace can become dangerous the same way that combustion of any kind in a home can create dangers. That doesn’t mean that it’s common, or that you should feel afraid that your gas furnace is always on the verge of becoming a danger for your family. The modern gas furnace is built to extremely high standards and must pass numerous government requirements before one can be allowed into a house.
Although odd noises coming from your furnace may be annoying, there is a good reason to be thankful for them: they can warn you when something is wrong that needs the help of HVAC professionals to correct. Furnaces aren’t yet advanced enough where they can automatically determine what their malfunctions are and communicate the data to their owners. Maybe someday we’ll have that technology. For right now, you’ll have to settle for paying attention to warning noises so you know to call us for 
