No, you should not stop pedaling when changing gears. On the contrary, you need to pedal when changing gears on a road bike. The chain needs to be in motion for the derailleur to shift from one gear to another. If you try to shift while coasting, you may damage your bike. However, you should take it easy on the pedaling pressure when you shift to allow the chain to smoothly transition to the next gear. Lastly, always be gentle with the shifters. Too much force can cause them to break.