Ted Eaton replyed here on an overheating thread that Ford did indeed use different pulleys in various parts of the country but did not mention A/C as I remember.
A test for you is to start the engine cold and let it warm up with the cap off and the tank about 1 to 1-1/2" low. If after it has warmed up to operating temp and you see no movement of water by looking in the tank; then just barely raise the idle and if you see movement install a smaller pulley.
My 56 ran hot at signals at idle and drove me nuts. I did the test above and there was no water movement. I bought a pulley and spacer kit from Summit for a 302 67-68 Mustang. It was chrome and I painted it satin black and my cooling problem went away. It was a little over 5" and mine was over 7". I also put a pipe plug in the bypass with a 1/8" hole drilled in the plug. I too will be adding A/C soon. Good luck.

56 Vic, B'Ville 200 MPH Club Member, So Cal.

I'm trying to determine if Y-block cars that came from the factory with air conditioning also came with smaller-diameter water pump pulleys than did Y-block cars that were not equipped with a/c.  A friend tells me that all GM vehicles of the same era that came with factory-installed a/c units had smaller-diameter pulleys installed that did cars without a/c.  The purpose, of course, was to increase the RPMs of the water pump and the fan to protect against over-heating at idle when the a/c is turned on.  If Ford did, in fact, install different size pulleys in their a/c-equipped cars, it would be very helpful to know the diameter of the different pulleys used by the factory for both a/c and non-a/c cars.  I'm researching this because I recently installed after-market a/c in my '56 312 c.i. Fairlane that came from the factory without a/c, and while it works well, the engine does heat up quickly on a hot day in slow-moving or stopped traffic.  A fix I'm considering is going to a slightly smaller-diameter water pump pulley and it would be helpful to know the best diameter pulley to use.  Thanks, Ron