No, just take a look at how long and smooth does a pinephone run with "GNU Linux" vs stock android.
Android devs actually backported a bunch of work to the mainline kernel with regards to low-level energy management, but that's only one half of the story. The other is your phone stopping unused apps gracefully, and being able to go back to sleep regularly.
The vast majority which lives in android userspace. The customer compositor, input stack, wlan daemons, etc, are all tuned and optimized for power efficiency. Also, these days, there is a lot of hardware controlled directly by userspace - it's not just the GPU. And those hardware are generally important for offloading a lot of conpute and reducing wake ups. Things seem to only be trending further in this direction.