Can I make a web site continue running when in standby?
HTML5 ServiceWorker seems to support what you need via BackgroundSync / PeriodicSync feature. However, since ServiceWorker is still an ongoing effort, I'm not sure what features are currently implemented in Chrome. I couldn't find any good demoes of this, only proposals: https://github.com/clelland/BackgroundSync/blob/master/explainer.md

Cordova has recently added support for Background sync: https://github.com/MobileChromeApps/cordova-plugin-service-worker-background-sync, but this requires you building an Android app.

Without browser's explicit support for such a feature, all your ad hoc efforts will be a waste of time, since your code will be guaranteed to work only when the browser is in foreground. Otherwise, the browser itself can be killed by the OS, and won't be able to continue executing your page's code. The periodic sync feature provided by ServiceWorker implies that the browser would schedule periodic jobs using the corresponding Android services, like you would do in a Java app.