The ship will not be able to fight without the superstructure. End of story. Radar, comms, everything: it's up there.
Actually, there are backups in each turret tower. It's an older system, but the main guns are fully capable of shooting and targeting on their own.
not to mention that with thing like wireless communication and stuff, ta ship can recieve targeting data from other friendly vessels without the need for a radar of it's own - and the recievers(s) don't even have to be exposed.
EDIT:
Also, the Yamato was a flawed design. It's waterline armor and bulkheads, as well as it's anti-air armament were laughably inferior to the Iowa.
The Yamato was large, but ultimatively poorly designed.
So saying "Yamato was sunk with 19 hits, so Iowa will be too" is like saying "The T-84 was destroyed by a RPG hit, so the Abrams will be too". They are different beasts.
Ultimatively, a battleship is a huge, juicy target - but then again, any large vessel is. It's not like planes for an aircraft carrier or missiles are exactly cheap these days.
The value of Iowas is as a shore artillery platform - it can lob
thousands of cheap and effective rounds. IIRC, each turret has a 700-round magazine. That's a lot of bang. Compared ot the number of missiles that need to be hauled and fired, and their cost, it has clear advanatages.
And a funny little fact - the Iowas were designed to protect carriers - form both enemy warships AND aircraft. They proved their worth by helping repel 4 enemy air attacks.