No, they just sit there if the power goes out.
As soon as you get above 5x turnover (100 US gallons per hour for a 20 gallon US tank) you would be ranging into the "overfiltering" catagory I would say. Remember, the thing to think about in a smaller tank like a 20 is that you have to think about your individual fish and plant species and consider whether they like begin blown around the tank (some do, some don't) You can turn the spray bar toward the glass which sometimes helps with high flow rates.
~~waterdrop~~
ps. When you have a power outage and you're staring at that cannister just sitting there, the first thing you should think about is getting a big bucket. You can take the output tube and lower it below the filter level and let about one filter volume flow through the filter to the bucket. Then pour that tank water back into the tank. Its ideal to do this about once ever hour to keep your bacteria alive (they need oxygen and ammonia) but they can withstand you getting about 5 hours of sleep and then doing the manual water thing again (assuming the power outage goes overnight.)