Hi Doug
Yes, you are correct about the Gemini refining any errors associated with a polar alignment.
I have always done an accurate Polar Alignment using the Drift method, my aim is to have a star stay within the central X-hairs of a high powered guiding eyepiece for at least 20 minutes or so with only drift in RA.
On startup, the Gemini uses the Counterweight Down position with the OTA pointing at the Pole, the more accurate this is, the better, although saying that, it does not really need to be absolutely perfect. From that position, the Gemini will go to a selected bright star, you then center that star using a X-hair and synchronise the system. From there on in, you go to at least 4 to 5 stars on that side of the Meridian and do what is called an Additional Align, the Gemini is then building a Pointing Model, all the time it is giving you A and E numbers (Azimuth and Elevation), these numbers are in Arc Minutes and are the distance the telescope is from the Pole. This is for a Cold Start.
You only need to Synchronise on one star for a Warm Start, then GOTO whatever object you want.
You then select other stars on the other side of the Meridian and continue to Additional Align, all the time the A and E numbers should be falling. You can use the Hand Controller or the current ASCOM driver or Gemini Control Center to show you the detailed results.
So, in reality, if you get A and E numbers of 0 and 0, you are within 1 Arc Minute of the Pole, if need be, you can use the PAC (Polar Alignment Correction) feature to get closer.
I have A and E numbers of 0 and + 2 on my mount and find that my Autoguider has no trouble correcting these.
Cheers