What does Linux do with existing files in a mount point?

When you mount a filesystem on a directory /mount-point, you can no longer access files under /mount-point directly. They still exist, but /mount-point now refers to the root of the mounted filesystem, not to the directory that served as a mount point, so the contents of this directory cannot be accessed, at least in this way. For example:

# touch /mount-point/somefile
# ls /mount-point/somefile
/mount-point/somefile
# mount /dev/something /mount-point
# ls /mount-point/somefile
ls: cannot access /mount-point/somefile: No such file or directory

There are ways to get a merged view of the mounted filesystem and the data that was already present, but you need an extra layer called a union filesystem.

Under Linux, there is a way to see the hidden files. You can use mount --bind to get another view of the filesystem where the mount point is. For example

mount --bind / /other-root-view

You'll see all the files in the root filesystem under /other-root-view.

# cat /other-root-view/etc/hostname 
darkstar

In particular, /mount-point will now be accessible as /other-root-view/mount-point, and since /other-root-view/mount-point is not a mount point, you can see its contents there:

# ls /mount-point/somefile
ls: cannot access /mount-point/somefile: No such file or directory
# ls /other-root-view/mount-point/somefile
/other-root-view/mount-point/somefile

It will just be mounted, and the files disappear, coming back when the folder is umounted.