Yes, with a testing server, you'll see changes made in your css that affect your included html in the parent page.
Modifying css in an attempt to see the change on the include file itself however, generally won't work. Even if the include had a link to the css file, it still may not actually show the css changes because the include isn't a page, it's just a fragment of a page, and many times won't have enough html for the css selectors to latch onto the way they're written.
1. Open one of the parent pages that uses the include
2. Make changes to the css that will affect the include's html
3. Click the "parent" page to see the changes.
You don't have to save the changed css file at this point, it should show the new css as soon as you click the parent page. If it doesn't F5 will refresh Live View and show anything that's been modified.