Let's look at it objectively:
You don't even need a battleship. Let's look at the first iron armored ships and their combat - which included frigates and 2 ironclads. The armament of both the frigates and the ironclads is comparable to somewhat superior to an age of sail ship of the line. USS Monitor and Merrimack/CCS Virginia in the Battle of Hampton Roads however showed what a mere 1 inch of wrought iron armor could do: Virginia got shelled by the Unionists frigates and wooden warships like crazy and suffered no damage. Monitor hammered away on Virginia and Virginia on Monitor and neither did do any damage to the other, not even dents at point-bank!
Now, you want to send a Battleship in. This battleship has multiple times the armor of these Ironclads and the ironclads hat better guns than a Ship of the Line! Taking the Bismarck Armor Scheme, the armor is 6.25 inches at the top deck and 12.5 inches of belt armor. Deck is 2 inches, impenetrable, and the whole ship was made from superior steel than the ironclads. The New-York Class has very similar armor and taking the Iowa Scheme, the Armada faces up to 14.5 inches or belt armor. Even the HMS Hood featured 6-12 inches of main belt armor!
But what about the superstructure? Well, the superstructure is, out of necessity to uphold the structure, made from at least half an inch of proper steel, which is roughly equivalent, if not superior, to zhe 1 inch of the wrought iron armor of the USS Monitor!
No battleship can be even be dented or damaged beyond the finish with Ship of the Line armament. Atop that, the cannonballs only deliver kinetic energy, while the Rhodney did shoot both much heavier and much larger ammunition that was either Armor Piercing or High Explosive. Without such large ammunition, heating the armor to any glow is impossible. The battleship at best looses its paint, and once it can raise steam, it just steams away, turning any ship of the line that is in front into driftwood.
Much more likely, the commander would observe the armada, pinpoint the flagship, and then sink that, and the ship of the vice-admiral, with 2 shots using secondary or tertiary armaments. Beheaded, the armada would have to see that there is NO safe area within miles.
Now, let's amp up the ante and replace Bismarck with Musashi: Captain Kaoru Arima spots the armada on the horizon. He has the fire control radar crew trail in the fleet sailing in a rather close formation. He decides to spend 6 shells per volley, one from each gun of the forward facing main batteries. The barrage of 6 times 46 cm (18.1 in), trailed in with the fire control radar over some minute, is launched with about 6° elevation. We start the battle-clock.
T+0:0:15 - The barrage of 6 shells reaches 10.000 meters and is some dozen meters above the waterline. Because he saw wooden ships, Capitan Arima ordered to load sanshikidan - combined shrapnel & incendiary anti-aircraft ammunition. The shrapnel is distributed in a 20° Cone from the detonation point, ripping through sailors, sails, and ships, further setting ships and sails ablaze with impunity. The zone of destruction for each shell is about 1 kilometer long and 350 meters wide at the end of the cone - and the 3 guns of each turret are aimed with sightly different points of impact (staggered to be about 500 meters from one another) for a total zone of destruction of twice 44080 m² (8.2 American football fields). ANY ship within these ~16 football fields is practically destroyed, and that at the expense of the most useless ammunition Musashi has abroad! In tight formation, that would be between 25 and 50 ships hit.
T+0:00:45 The second barrage is launched, aiming a few degrees more port and starboard.
T+0:01:00 second barrage sets another 16.2 football fields ablaze before the enemy fleet even has had the chance to even react by setting any signals. The first ca. 20 ships following up on those already set ablaze run into the floating and burning wrecks as they can't maneuver quick enough, suffering damage. Total number of disabled ships is between 70 and 120 at this point
T+0:01:30 Third barrage launched, distance to the armada is still very close to 10 kilometers.
T+0:01:45 Third barrage hits. Following my estimate, between 16 and 27 % of the armada has been disabled. If the rate of destruction is kept up, the armada will be wholly ablaze between T+0:08:15 and T+0:12:30. By this time the Armada sailing at 6 knots would have managed to close in towards 8.5 km/7.5 km - or several miles outside of their engagement range.
Note that he could have started fire at 25 kilometers and still most likely hit his target, 10 kilometers is guaranteed hit area for Musashi (and maximum range for the anti-aircraft ammunition), and anything below about 2500 meters is pretty much elevation 0 for the main armament.
The secondary armament of 15.5 cm guns has a depression angle of -7° and is mounted at about 15 meters above the waterline. It can hit ships at their waterline starting at 122 meters - which is closer than the effective range of the ships of the line, meaning any ship trying to get that close gets immediately sunk, either by an armor-piercing shell cleanly ripping through the boat twice, starting to flood it or by a high explosive load of 50 kg blowing up the ship's hull and the magazines.