Sound is a mechanical wave that has to have a medium to travel through, such as air waves. There is an interesting phenomenon that occurs when waves encounter each other, called interference. Interference with sound waves can be both constructive or destructive. In the case of your question, we would be interested in constructive interference, where sound waves of similar wavelength and frequency would overlap each other, producing a higher amplitude, or higher position from the rest position of the wave. This is what amplifiers do for electric guitars, they increase the amplitude of the wave. What is the result? A louder sound, of course. I will never forget the first time I attended a major college football game, with close to 100,000 people in attendance. The first time the band played the school fight song, everyone started cheering, and you could feel the ground shake! So, to answer your question, can enough people making sound together impact the Earth? You bet they can, if their voices all constructively interfere with each other, producing one giant sound wave.
Sound can produce vibrations in other objects due to resonance which takes place when the frequency of the sound matches the frequency of the object.
When people shout, their sound have different frequencies and these are originated at different places. The amplitude of the sounds of same frequencies can increase if they are in-phase with one another and this cannot happen due to distance that reduces the amplitude. The net effect is going to be a combination of sounds of various frequencies and amplitudes. This will cause nothing but noise pollution on earth for the time they are shouting.
In addition all the shouting people may have bad throat if they shout for a very prolonged time.