When I had my last boat, before I installed a water heater bypass kit on it, you had to fill it with anti-freeze to winterize it.
And in the spring time, I had to run water through it for about 30 minutes before it was clean enough for my satisfaction.
Even now, I run water through the lines for a good 20 minutes to ensure they are clear.
So, yea, for the little amount of water the ice maker uses for each load, I think you would be making ice for a month before the lines are fully purged.
You can buy one of those Antifreeze Refractometers and test the water as you purge the lines to see how much antifreeze is left in the lines. You can buy them on Amazon for as little as $25, all the way up to $150.
Get one that can measure Propylene Glycol (the pink RV stuff). Many of these refractometers will measure both Propylene Glycol, Ethylene Glycol (the normal green engine antifreeze), battery and brake fluid.
Like this one:
I plan on buying one in the near future. Since these are basically used to measure protection rather than residual antifreeze, the scale is calibrated in degrees of protection rather than PPM, but the bottom of the scale is 0% (no protection) I would think means no antifreeze remains.
Camco makes a refractometer, but it's over $100. And since some of the the $20 ones can measure Propylene Glycol, seems the cheap one should do the trick.
I see this could be useful not only for winterization to make sure you have enough antifreeze in the system, but also for spring commissioning to make sure all of it has been purged.
Anyway, seems yet another handy tool RV'ers should have.