Yes.
Apparently OS X builds a temporary thumbnail using the actual contents of the file. It does this for all files, whether they are image files, word processor files, TextEdit files, Pages or Numbers files, etc.
It does not add a thumbnail, or custom icon, to the file - it just uses the file content to make one temporarily.
This means that when the OS is displaying an alias, it looks inside the alias for an image to use to build a temporary thumbnail. Since there is no content to an alias (an alias is nothing more than an icon and a pathname to the original file; it has no content), the OS is forced to use the 'native' icon for that file, which is the native icon of the original file, meaning the default one used by the program that created the original file.
When an actual thumbnail (custom icon) has been created and embedded in a file, that is used by the OS for display. And, since a file's custom icon is applied to an alias made to that file, the alias then also displays the custom icon (thumbnail).