I assume if the fact that power saving turns off mobile data, if I had it turned on over night I would miss any texts during that time, right? (Meaning, the phone wouldn't alert me when it is sleeping with the screen off)
Well, the device consumes extremely low power from the battery if it's left idle overnight while connected to WiFi anyway. Do you really need it to be on power saving mode overnight?
But to answer the question, you will miss texts, yes.