Not even remotely.

Take the following link which is part of an Defra (UK gov) funded initiative called 'Trees Outside of Woodlands' and constitutes a public map showing lone trees, groups of trees and small woodlands across England.

https://ncea.maps.arcgis.com/apps/instant/sidebar/index.html...

How could it be? Growing up, there was a large horse chestnut tree that was a meeting point for all the kids in the neighborhood. It was such a huge part of our lives that it became an icon for our childhood, as several others have agreed with me as adults. It's gone now, as it grew old and diseased and someone cut it down. But it was a very significant tree for many people in the town for many years. I doubt, however, that it, or so many other trees that had similar impact on people, would ever make a Wikipedia list. There are just too many trees.

No, but you can add anything missing if you have a source!

It can never be. There are many notable trees, but some of them will never have a Wikipedia article.