No, and it might even make you burn fewer calories!
The power (energy per second) that you put into cycling is spent in two ways:
- Overcoming "rolling resistance" (e.g. flexing the tires)
- Overcoming "wind resistance"
At about 20 km/hour and above, "wind resistance" is the larger/dominating term. It increases as the square of the speed (so, e.g. to increase your speed by 20% would require 45% more power).
Anyway, the canonical way to spend more power into a bicycle is to travel faster.
To go faster you might want to pedal more rapidly in a lower gear (the "cadence" of your pedalling should definitely be above 60 cycles per minute ... maybe 90 or more with practice and with clips or cleats on your cycling shoes). It's better to spin faster with medium force that spin slower with big force ... if the pedal-spinning slows below 60/minute then you need a lower gear.
Anyway, once you're cycling (after you've warmed up, e.g. after the first 20 minutes) you ought to be getting wet, either because it's raining or because you're sweating. Generally you'll be hot and sweating. One of the things that makes cycling bearable (or pleasant) is that there's always a wind when you're cycling ... and that wind helps to keep you cool. Cyclists wear "moisture-wicking" clothing which helps to keep them cool (helps sweat to evaporate).
One of the limits, one of the things which may limit how much work you do, is how hot you get and how quickly you can shed that heat. Imagine: you could work harder in a hot gym in front of a cooling fan than you could without the wind from the fan. Similarly you can bike harder if you don't get too hot, and if you start to get too hot then you have to stop or slow down (or risk heat stroke etc.).
So, don't wear a "weight vest" which would keep the heat in and not transpire. Wear lightweight clothing and cycle faster.