While some data on which tabs you've viewed is synced, that's not accessible from extensions, and you certainly can't do anything on the device with it from your computer (e.g. you can't throw up a block page, or fire notifications on the device). More importantly though, the data that does exist exists only for which Chrome tabs you've viewed, and the key thing for mobile devices is to be able to block apps too. It's definitely going to require a project in itself.
Ideas
You don't need Android support. Desktop Chrome syncs with Android so the data is already available you just need to figure out how to access it
I'm afraid it's not that simple, sadly.
While some data on which tabs you've viewed is synced, that's not accessible from extensions, and you certainly can't do anything on the device with it from your computer (e.g. you can't throw up a block page, or fire notifications on the device). More importantly though, the data that does exist exists only for which Chrome tabs you've viewed, and the key thing for mobile devices is to be able to block apps too. It's definitely going to require a project in itself.