If one were to get a good 3 star alignment and then park the scope in the home position and turn the scope/mount off, do you need to do another 3 star alignment if you power up the next night?
I'm running an EQ6R. The obvious answer is "just try it out!". Alas, I can't observe until winter as we live in the woods and the leaves obstruct the sky.
IIRC, the EQ6-R has a mode to reuse the previous alignment upon powerup.
However, if you're doing astrophotography, you can skip the star alignment process (but not polar alignment) and use platesolving to find your targets.
Basically, your control software will match the star pattern in the camera image against a database, using the mount's reported estimated position, as a starting point, and in a few seconds it will determine the actual location to arc second accuracy, so that the next goto should centre the target accurately.
You can experiment with this using the free Demo of Astroart 8:
just lookup plate solving in the help file.