I saw in BeerSmith you can check the box to account for the tun temp in the strike water. Is it pretty accurate?
Yes, but it doesn't hold the temperature as well if you don't preheat the cooler MLT. I will lose about 6 degrees in an hour with a non-preheated cooler vs one that is preheated. In a preheated cooler, I lose about 1 degree over the course of an hour.
Why do you need to pre heat the mash tun? I heat my strike water in the mash tun, then when the water hits about 10 degrees above my target mash temp I dough in. Am I doing something wrong?
This IS preheating. You're adding hotter water to the MLT, and letting the cooler absorb the excess heat. Then mashing in when the water cools to strike temperature.
It really depends on where you store your MLT, but as an experiment try adding 1 gallon of hot (NOT BOILING!) water to it. Make it 180 degrees at the highest, to avoid warping and cracking. Stir up the water, and take temperature readings. It will drop 10 degrees or more, really fast. Then, it will hold the temperature after that. That's what you want when you mash as well.
I add 180 degree water to the MLT, and give it about 15 minutes to cool to strike temperatures. By then, the MLT is nicely preheated and then when I mash in, it holds the heat quite well.
Also, the bigger the mash is, the more stable the temperature, especially in a big cooler. A 7 pound grainbill will lose temperature more quickly than a 20 pound grainbill in the same sized cooler. Preheating really helps with the smaller grainbills.