The road is practically a forest service road. It's poorly maintained and kinda hairy at times, that's why they reccomend chains. Lots of dudes in wheelin' trucks like yours just roll up there no questions asked. I drove a regular pickup up, took my old Benz up there with just winters on it a couple times when it was snowing, and timmytard and I even drove up in his old fwd car that had a little spare on it I think at one time.
They don't check, AFAIK