Yes, the '02 silverado uses a low pressure cutout to cycle the compressor, maybe it's formally called a compressor cycling switch. And it has a high pressure cutout switch. These are just on/off.
My truck is a '99 s10 with a 2007 5.3 and a 2002 silverado calibration in the pcm. The fans turn on and off fine by engine temp as stock as it gets having been converted. Now adding a/c adds a ton of confusion to it because the pcm wants to see pressure. I've noticed on my camaros that the low fan is almost always on with the a/c and the high fan kicks on and off frequently.
I live in Florida and built this truck without a/c during the cooler months and when summer came I hardly drove it because it was so hot out. I put a/c in it.
I tried the transducer but I already had my fans set up to run second stage only, meaning once the a/c runs a minute or two the fans come on high speed, so not wanting to rewire my fans I just added a relay activated by the a/c request wire. This relay grounds the main fan relay when the a/c comes on. The reason I did this is because I didn't think my fans would keep up with it all. I had the stock thermostat at first and it would run at 205 degrees, so once it got heated up the fans would run all the time anyway.
Now I have a 160 degree thermostat and my fan settings are on at 192, off at 190, and they actually cycle. So with this thermostat and the fans actually cycling I have put wiring the a/c fans through the pressure transducer on my to do one day list also.