Do Google spam reports ever work?

In most cases spam reports are used for future algorithm updates so Google can detect spam automatically. They are not going to manually remove a site from the index based on spam reports but their is a good chance there will be a manual review. You are better off submitting any spam reports through Webmaster Tools as Google considers these to be more legitimate and of a higher value than an anonymous user filing one. The goal is to find the spam on the site in question and develop a way for their algorithm to find it mechanically and then discount that technique or possibly filter or penalize the site. I would not hold your breath if you are waiting for a spam report to cause a quick change or in some cases any change as some sites may be ranking well in spite of spam instead of because of it.
JohnMU wrote a bit more about spam reports over at the Google Webmaster Group.

It's definitely hit and miss. Google may take action against the site, but it may not be the action you expected, so may look like they ignored your request.

Matt Cutts recommends using the report spam link within Google Webmaster console. Apparently those are looked at more carefully.