Construct 2 does have an update notification! It just tells you when a new version is available, but won't download it for you (see that thread).
However sometimes I delay setting off the autoupdater till a few days after a build is out. If there's a big problem I won't trigger the autoupdater at all and will wait until the next build when it's fixed instead. If a few days have gone by and the release seems to work OK, then I set off the autoupdater. Then, it takes up to 24 hours for the software to check for an update again and alert you.
So you should see prompts even if you never visit the site.