What is the best way to determine whether an extension is likely to be compatible with a contemporary Civi version rather than just not updated to reflect as much?
The best practice for upgrading is to upgrade a copy of your site on a "staging" or "development" server. That's a good time to test your extensions to see if they work.
Short of testing the extension, I don't know that there's a good way to ensure an extension works. However, you can:
- Read the code, if you know how. If it's all (or almost all) using API calls rather than BAO calls, you're probably safe.
- If you DO determine it to work well, post an issue on the ticket tracker for the extension (usually on Github) saying you tested it successfully with the latest version.
There's a volunteer extension review team, and their job mainly covers reviewing new extensions, not existing ones - but if there were more people, we could do this sort of testing!
With regard to this particular extension - it's mostly BAO calls, not API calls - but there's so little code, I'd be pretty surprised if it didn't work as-is on version 4.6.
If you go to the Extension page eg https://civicrm.org/extensions/civivolunteer then you should see a RELEASES section near the bottom which states what version of CiviCRM the extension is known to work for. This may be obvious, but your question doesn't explain what you have already done to check.