no there was significant burn caused by that fire especially below the eastern rim mostly on Apache forest (and reservation), but not in any area of the rim it seems you plan to visit. that's 100 miles east at least. and by "a few places" i mean given the immense size of the fire, about 30% was burned north of the escarpment and mostly held south of the 260 highway.
To get to the Rim from Tonto Valley area, you'd have to drive the entire length of the az188 or go west until you hit the az87 and north past Strawberry. You wouldnt encounter much of the Dude fire unless you hiked a large chunk of the Highline Trail or were at small spots on the rim, east of Geronimo camp and such. There's still an enormous area of land that is pristine, hasnt seen logging for decades, or fires. Bark beetles, that's another story (a sad one)