Does iPhone 'Low Power Mode' actually give a longer battery life?

Personally, I have not seen a change…

It should but I never actually use that, I just charge it.

Yeah it does

Yes, it will extend your battery life by a few minutes but in reality it's not that big of a deal. If you ever get that pop up saying it entered power mode, just plug it in. If your device is low on power and you don't have access to a charger, I suggest buying a portable charger.