Interesting idea. Certainly a large percentage of our smartphone usage is turning on the screen to glance at a notification, then dismiss it. Smartwatches allow you to not have to do that. But the notification still comes to your phone, and still needs to be beamed to your wrist. So you don't save on any network usage battery. It's basically only the screen. Now the screen is expensive, no doubt. But even so, how much additional battery life would you get out of a phone from turning the screen on 50 times less over the course of a day?
I don't think it's really about getting more life out of the existing battery. I think it's more about better integration with people's lives. E.g., I don't want to have a fit of beepilepsy every time I get a text or a calendar notification. Glancing at the watch is way better.
But as a side effect, I think moving a bunch of watch-friendly things to a watch will let you make the phone bigger. That won't reduce total power usage, but it will increase power availability.
The modern smartphone is a huge compromise. It has to do everything but it has to fit in our pocket and run all day. It's basically a Swiss Army knife: sure, it does everything. But it doesn't do anything very well.
I think the trend toward larger phones is exactly why wearables will be big: If you can have the little and low-interaction things on your wrist, then that lets the phone change to be better for the tasks that remain for it. A bigger screen and a bigger battery are more appealing if the phone only comes out when you actually need a big screen, rather than just to check the time or to acknowledge a text.