When updates would roll out for Google devices, a certain percentage of people get the update and then the rollout stops until the next stage. Check for updates as many times as you want, but it won’t help you get the update faster.
Now things are a bit different, and for the better. Googler Elliot Hughes says that the new system allows the “Check for update” button to pull the latest software version, even if a specific stage of the rollout is over and everyone designated to get the update has already gotten it.
To take advantage of this change, you need to be running the latest version of Google Play Services. And of course, it’s unlikely this will be the case for phones other than Google phones, but it’s worth a shot. We all mash the update button anyway, but now it might prove useful.