Can you drive the entire Mormon pioneer trail from navoo to salt lake?

Not exactly. Similar to the Oregon Trail, many portions of the Mormon Trail have been swallowed up by development projects to accommodate a growing nation.

That said, there are still places where portions of the trail are still visible, including ruts from the wagons used by the pioneers. Also, a visitor center currently exists in Council Bluffs, Nebraska that explains the Mormon exodus very nicely.