The button will not work when power is off, that's just common sense. It is force sensitive which means it requires software. The new MacBooks with the same technology do the same thing. When you try to "click" the trackpad when the power is off nothing will happen. It's not a physical button.
Ha so funny. No. I'm an advid believer of doing a hard reset after installing updates. Whether it be a beta update or final release. Because of the frequency of beta updates I do it quite often. A hard reset kills off any indexing going on in the background after an OTA update.