I really don't think so. Turning on "Don't keep activities" prevents apps from running in the background, which helps keep Android in sleep mode. From what I've seen, most poor battery life is due to Android staying awake while the display is turned off, so turning on "Don't keep activities" helps prevents this.
You can see in my battery usage from today, most of the time my phone is only awake when the screen is turned on. It's near the end of my work day, with 2hr4min of SoT and I'm still at 56% battery, because when my display is turned off my phone stays asleep.
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