No. Thumbnails illustrating the data in a shapefile, coverage, or feature class should be represented using the default renderer that is used by Geography view. The dataset itslef only contains data, not symbology. Therefore, its metadata should not contain information about symbology.
Layers, in contrast, define symbolization, labeling, display, and query information but they do not contain data. A layer file's thumbnail will show the symbology it uses to represent the data. Its metadata should describe the information that is portrayed and how the attribute values were classified. A layer's metadata should not describe properties of the data such as its coordinate system.
To describe a dataset in more detail, you can create separate graphic files that illustrate how the data can be symbolized. You can reference those graphic files in the metadata as “Browse graphics”, or add them to the metadata as image enclosures. With some stylesheets the referenced graphics can be viewed via a hyperlink and thumbnails of image enclosures will be shown.