Not exactly.
You could use a Frame that goes to the edge and have that part of a style.

You could use Font shading to get your color and turn it off for the text, I believe. I have not tried this.
Here is my page on Frames and Textboxes. It shows how to insert a Frame in current versions of Word.
Frames and Textboxes in Microsoft Word
Here is a link to a document using this method.
Dropbox - Heading1Frame.docx