I am really scared to jump into this conversation as there are different specifics on each setup but...
The autopilot is somehat dumb - It doesn't calculate stuff. It is commanded. Normally there are three things that can command the autopilot.
Heading - this is simply the user selecting a heading or often just pressing the "auto" button. The "dumb" autopilot will simply steer that heading.
- If installed the wind
instrument provides a "changing" heading to the autopilot - It is still basically a heading to steer that changes as the Apparent Wind changes
GPS - The GPS (or more acurately gps/plotter integrated unit) sends "CTS" or course to steer. CTS is computed inside the GPS and is based on XTE from a pair of waypoints.
Speed is often used by the GPS to calculate CTS - If you are close to the waypoint, far off course and going "fast" the CTS angle will necessarily be larger.
Having used GPS in flying at much higher speeds this effect is more apparent than on a boat.
How the autopilot is controlled depends on the setup - that is if there is a chartplotter
that is receiving GPS input and the chartplotter holds the course etc. In this case the plotter is sending the CTS onto the network which is received by the autopilot. The GPS in a "plotter" setup is usually a "dumb" gps receiver that only provides position info to the plotter. The plotter in this case is where the magic is happening.
I don't know what happens when two plotting devices are hooked up in the same network - I doubt that is a good thing.
In the original question OP asked about more precise steering
. The GPS won't improve that. Every autopilot I have encountered has a steering
calibration. Increasing the steering sensitivity may reduce XTE but will result in more "hunting" and more work for the autopilot with an increase in load and electricity consumption
In a sailboat the toughest point of sail for an autopilot is downwind in a quartering sea. But that is the toughest for a human as well...