Yes, the Italian 15" should still have ~560 m/s at 20km. At 20km the Italian gun has virtually the same vertical armour penetration as the German 16"/52 despite less weight and a smaller caliber. Its not to say that such factors as weight and caliber are not important, they are just less important than striking velocity and head shape.
There is discussion included in R&R that is related to your other thread about British thoughts about fighting range. They concluded that for longer fighting ranges a heavy shell of the same caliber held the advantage against vertical armour, but at short and medium fighting ranges a higher velocity gun was better. To illustrate the concept the British were discussing we could compare the USN 16"/45 with the 2700lb shell to the USN 16"/45 with the 2240 lb shell. At 18k yards the older 16"/45 gun with higher MV had superior vertical armour penetration performance by about 5%, but at 28k yards there was no difference, and beyond that range the heavier shell will be superior. This is due to the greater velocity retention of the heavier shell.
Head shape also plays a role as the range increases against vertical armour. As the striking angle increases a blunter head shape will perform bettter and better relative to a sharper head shape. The KGV 14" with a sharp head shape could get equal or better performance compared to 15" and 16" at 12,000 to 16,000 yards battle range, but at 25km it would be inferior. However, due to the lighter overall shell weight, at 25km the 14" gun is getting a steeper angle of fall than a 16" gun of comparable MV. This is due to the lesser velocity retention of the smaller and lighter shell.
That same concept applies to the German 38cm vs the German 16"/52. At 18km the 38cm has within 3.7% the vertical penetration of the 16"/52, but from 25km to 35km it actually has superior deck penetration.
Entering a night sea battle is an awesome business.The enveloping darkness, hiding the enemy's.. seems a living thing, malignant and oppressive.Swishing water at the bow and stern mark an inexorable advance toward an unknown destiny.