The closest I think you could get is with cell styling, but it does have its problems.
If you wanted to try it though, it is simple enough to put in place, simply
Table > Insert Table a 1x1 table in your text frame. Put whatever paragraph you want to have a fill/stroke inside that cell, then open your
Window > Styles > Cell Styles panel, and create a cell style. You can assign a fill and stroke, apply this style to multiple cells, and edit the style at any time to have changes applied to every instance in your document.
- The cell will auto-adjust its height to fit your content, but the width is static after its creation. If you change your column/page-width, you'll need to manually adjust cell width.
- In terms of document flow, the whole cell is a treated as a single character within the parent text frame. If your paragraph (without being inside a cell) would typically span between columns/pages, the whole cell will be forced past the break point, leaving you with some blank space at the bottom of your column/page.
- Selections inside your text frame will also treat that cell as a single character. This makes it a little more tedious to make edits since that paragraph content has to be interacted with separately than the content before or after it. This is less tedious with proper Paragraph/Character styling applied though since many edits can be made to the style instead of the content directly.
Object Styles (
Window > Styles > Object Styles)
As suggested by @John-Manly, it is easy to just draw a background box. Additionally, you can set an Object Style so that you can apply/edit that same style for boxes behind multiple paragraphs.
However, if your text flow or paragraph size changes, the background box will no longer be sized/positioned properly.
This is likely a poor solution based on your initial request, but if you can do without left and right stroke, and without a background color, you could define Before and After
paragraph rules in the paragraph style box. This will put horizontal lines above and/or below your paragraph automatically.