Let me ask, how many of you answering here have tested this yourself?
In real life tests comparing two pairs (one set of Dell laptops with N4200 chip and one set of HP laptops with Core i5) of identical machines with both OS', W10S boots faster and lasts longer than W10Pro, even at baseline configuration.
Do notice that the changes might be more or less noticeable depending on your HW configuration, but in the test the Intel Core i5 chip shows little difference in battery life with only a few minutes less for the Pro on average, while the N4200 on W10Pro takes a more noticeable hit of over half an hour on average.
Again, after installing apps the W10Pro on Core i5 loses only 10 minutes to the W10S, while the N4200 falls behind even more with an hour or more less battery.
To wrap it all up, with applications installed, the W10S had on average 15% longer battery life and up to 80% better boot performance.
So, yes. Installing x86 apps will most likely make your computer drain the battery faster. However, Windows 10S and Windows 10 Pro with baseline setup is not exactly the same as others here claims. As the actual HW in your system might also be a key to how big a difference you would actually experience, it would be impossible to predict exactly how your system would be affected upgrading to Pro. I use the CPU to differentiate here, but it could very well be other components that are causing the difference.
Update: One more thing to remember is how x86 applications tend to clog up the OS/registry over time. Comparing two identical systems after a year could show numbers even more on in favor of the W10S OS.