Anyone's CAs can engage battleships. But even the ridiculously powerful USN super-heavy 8"/55 shells have to close to virtually point blank ranges - 9.8km to punch through 10" of armor. QE and her sisters have 13" main belts.
Well yes - they certainly wouldn't count on penetrating the main belt. That's why I said any damage would be limited, but-
They will still be able to smash gun directors and superstructures.
This. Remember that Cesare herself was temporarily put out of the fight by a lucky hit
to her smokestack. Hardly the most armored element of a ship.
The idea of a heavy cruiser closing the range to where they could do significant damage to a battleship, even a WWI rebuild like Barham, is pretty suicidal. Even if the battleship's main guns are on local director control, thinking of 12 to 15 inch guns shooting at a target within 10,000 yards with only heavy cruiser armor, makes me think of a replay of Matapan's night action.
They would never get that close. The insanity of closing to point blank range of a battleship with a cruiser aside, Italian doctrine was radically different from the British one in that it called for methodical fire at an ideal distance of 20k yards and no closer - at least until getting a few significant hits in - as opposed to British tactics which focused on charging in and prioritize rate of fire at the expense of accuracy.
Reportedly, neither side was impressed by the other's gunnery in fleet actions.
EDIT: also, the 203mm/53 caliber guns the Zaras used had a theoretical 34km range. Of course they aren't gonna hit anything at that range, but they probably aren't gonna sit at 10km, either.
I don't think even the fire directors on the Zaras can get a firing solution at that distance, but Italian optical fire control was quite good (for reference, the optical fire control on Bismark was basically an improved German version of one of the first Italian BB FC sets - and the later Italian sets were marked improvements on the first version) and the Italian heavy cruisers OTL scored hits as far as 21-24k yards, while a
light cruiser, Montecuccoli, scored the longest ranged 6" gun hit of the war at
23-26k yards. That's what I mean by being able to engage at battleship ranges.
What the Italian cruisers will most likely do is bully the British battleships screening elements. Hurt as many of the Brit cruisers as much as possible to open holes to allow the Italian destroyers and torpedo boats to close to where their torpedos will have the greatest chance at hitting the British battleships.
The Andrea Doria, Caio Duilio and the Cesare are there to keep the QE's collective interest until the British go "Dude where's my escorts?"
This is probably going to be the most probable plan of action for the
Regia Marina (though it's unlikely we'll see torpedo boats taking part in a fleet action), yes. Though with the Third Cruiser Division being their usual selves, I expect them to take potshot at the BBs if they get the opportunity.
I am under no illusion this is going to be easy for the Italians, though. As I said, I foresee feels from both sides.
@Skywalker_T-65 Incidentally, what's the ITL status of cruiser Montecuccoli? The 'most haunted ship of the fleet' seems like a good subject for an omake. Armored Cruiser San Giorgio, too.