Yes, slicks grow at speed, and yes it depends on wheel width, tire pressure, tire style, size, and tire brand. Looking at finish line photos it looks like around 2" with the Goodyear 31x12x15 on 12" rims.
One of our JrFuel racers, didn't like running the GY D2585 on 12" rims, because they didn't grow enough, so he ran 11" rims unless he needed more bite and then ran 12". He was using a shorter stroke 387 ci SBC, and his motor was out 50", different combo than ours.
My experience has been mostly with 31x12x15 GY on 12" rims because we seem to need the 12" traction. When I'm deciding on gears and tires, I use one of the online formulas. Because I use a RacePak I can see what RPM we get thru the lights, I have found the computer and the online formula is pretty correct, because of converter slipage it makes up for tire growth. I found I just need to add 1/2" to the 31" tire to get the numbers to add-up to the RacePak.
Just figure the tire size with no or very little growth to get your gear change RPM. If you don't have a data computer, try using a GoPro aimed at your Tach, or get a play-back tach.
Jon, 800-624-3803