There is a possibility that this could be a devastating attack.  From a source who seems a bit odd, but who summarizes clearly what is alluded to in various other sources . . .

The Sunburn can deliver a 200-kiloton nuclear payload, or: a 750-pound conventional warhead, within a range of 100 miles, more than twice the range of the Exocet. The Sunburn combines a Mach 2.1 speed (two times the speed of sound) with a flight pattern that hugs the deck and includes "violent end maneuvers" to elude enemy defenses. The missile was specifically designed to defeat the US Aegis radar defense system. Should a US Navy Phalanx point defense somehow manage to detect an incoming Sunburn missile, the system has only seconds to calculate a fire solution not enough time to take out the intruding missile. The US Phalanx defense employs a six-barreled gun that fires 3,000 depleted-uranium rounds a minute, but the gun must have precise coordinates to destroy an intruder "just in time."

The Sunburn's combined supersonic speed and payload size produce tremendous kinetic energy on impact, with devastating consequences for ship and crew. A single one of these missiles can sink a large warship, yet costs considerably less than a fighter jet. Although the Navy has been phasing out the older Phalanx defense system, its replacement, known as the Rolling Action Missile (RAM) has never been tested against the weapon it seems destined to one day face in combat. Implications For US Forces in the Gulf

The US Navy's only plausible defense against a robust weapon like the Sunburn missile is to detect the enemy's approach well ahead of time, whether destroyers, subs, or fighter-bombers, and defeat them before they can get in range and launch their deadly cargo. For this purpose US AWACs radar planes assigned to each naval battle group are kept aloft on a rotating schedule. The planes "see" everything within two hundred miles of the fleet, and are complemented with intelligence from orbiting satellites.

But US naval commanders operating in the Persian Gulf face serious challenges that are unique to the littoral, i.e., coastal, environment. A glance at a map shows why: The Gulf is nothing but a large lake, with one narrow outlet, and most of its northern shore, i.e., Iran, consists of mountainous terrain that affords a commanding tactical advantage over ships operating in Gulf waters. The rugged northern shore makes for easy concealment of coastal defenses, such as mobile missile launchers, and also makes their detection problematic. Although it was not widely reported, the US actually lost the battle of the Scuds in the first Gulf War termed "the great Scud hunt" and for similar reasons.

Saddam Hussein's mobile Scud launchers proved so difficult to detect and destroy over and over again the Iraqis fooled allied reconnaissance with decoys that during the course of Desert Storm the US was unable to confirm even a single kill. This proved such an embarrassment to the Pentagon, afterwards, that the unpleasant stats were buried in official reports. But the blunt fact is that the US failed to stop the Scud attacks. The launches continued until the last few days of the conflict. Luckily, the Scud's inaccuracy made it an almost useless weapon. At one point General Norman Schwarzkopf quipped dismissively to the press that his soldiers had a greater chance of being struck by lightning in Georgia than by a Scud in Kuwait.

This latter part gives support to your argument that it will be difficult to find and destroy the missile launch sites.  Even should fixed C&C facilities be destroyed, there's no reason why mobile missile launchers would not be able to find and sink US Navy assets in the coastal environment, unless the US Navy withdrew to the Indian Ocean.