Good4it, think about how music is mastered. Every TV show, movie and musical performance is recorded with multiple microphones, and often artificial sound effects are added. An engineer takes the recordings from each source and puts them together in a single soundtrack.
A soundtrack can have only one channel. It's called "mono".
Most music has 2 channels: Left & Right, "stereo".
Most TV/movies have 5.1 channels: Left, Center, Right, Left Surround, Right Surround, and subwoofer.
In each case the engineer decides what he wants you to hear. Usually for music, he pretends you are sitting in the middle of the venue, several rows back from the front. So if the guitar or violins are on the left side of the stage, he puts their sounds in the Left channel. Instruments on the right go to the right channel. Instruments in the middle go equally to the left & right, so your brain interprets that sound as coming from the middle.
For TV/movies, and engineer does the same thing. Since usually the speaking character is on the screen directly in front of you, his voice is put on the Center channel. Various other sounds like doors opening, floors creaking, doorbells, jets, etc. should seem like they are off the screen to the left or right, or even behind you. So the engineer puts those sounds in the appropriate channels.
Dialog is primary in most all TV/movies, so the Center channel is used a lot. Much more than any of the other channels. If you don't have a center speaker, your AVR will send the center channel sounds equally to your Left & Right speakers. An identical sound at equal volumes and equal distances from your Left & Right will be interpreted by your brain as coming from the middle. It's called having a "phantom" center.
Most audiophiles like to listen to stuff in the same format with which it was mastered. If the engineer mastered the recording in stereo, we listen in stereo. If he mastered in 5.1, we listen in 5.1. Your AVR can artificially convert one format to another, but it is artificial and not as intended.
So the short answer is: No, you don't need a Center speaker for most music, but you do need it for most TV/movies.
