Do unused components on an object affect performance?

Example: I have a prop which sits in my scene being a prop, it had the animation component added automatically (and so did the hundreds of other props in my scene right now)

I never plan to use it since this is a prop and will never do anything.

Is it necessary to remove the component, or are the effects too minor, or has no effect on performance?

If the animation component is causing the prop to animate then it will have an effect on the performance of the game assuming it was set to play automatically. If you don't have the update doing anything on those objects, and they aren't automatically animating when you start the game there probably won't be a performance hit, or at least an extremely small one. The only thing that this will cause is the game code/ setup is a little less clean so it might confuse other developers.

My question to you is why does the animation component get added to the prop in the first place, I have never had that happen for things that I have imported that didn't contain an animation of any kind.