I've got a 285/50/20 on my escalade. Compared to mine, your 285/70/18 is going to be 1.39 inches taller, .79 inches skinnier than mine, Your side wall height 1.69 inches taller than mine as well. So yours a tad taller, and a tad skinnier than what i am running. I have no issues with my 285/50/20. i have factory takeoff 20's from a denali truck/yukon and they are 9.5 inches wide. I dont scrub or anything when turning, i had to crank my torsion bars just a tad to or on certain bumps, my tires would scrub the fenders. Is your truck 4-wheel drive? IF it is, this may concern you, chevys 4x4 trucks have an issue with offset, the front wheels stick out farther than the rear wheels. To the point a spacer is needed for the rear to match the front. Mine has that bulldog look from the front and the railcar look from the rear...
All in all, you should be fine with a 285/70/18 on your truck with a torsion crank. Since yours is a skinnier tire than mine you shouldnt have any scrub issues when turning full lock. The top image is the stock wheel/stock tire, the bottom is the new wheel/new tire. Notice the rear differences and double that for the front. So the front sticks out about another half inch or 3/4 inches.