Tapping the “Check for Update” button on Nexus/Pixel will actually be useful now5
More importantly, pressing the “Check for Update” button will not help you at all unless you've been previously selected for the rollout group. Google explained a while ago that the first time an Android user taps the update button, it determines whether or not he/she can download a new update.
Since only 1% of devices are usually selected to get a new Android update in the first 24-48 hours, it's quite easy to miss the opportunity. Subsequent taps on the button won't do anything until the next batch of devices is scheduled to start receiving the update.
The good news is things have changed, as Googler Elliott Hughes points out in a post on Google+. According to Hughes, as long as you have the latest version of Google Play Services installed on your phone, you can bypass the 1% limitation when you tap the “Check for Update” button.
Unfortunately, the new update system will only function for the Nexus and Pixel smartphones. Other smartphone brands pushing Android updates to their devices will continue to use their own methodology.