Would wider triple turrets force a much larger battleship hull?
Short answerThey affect beam, but separating machinery and magazines can simplify the protected internal layout and offset part of the penalty.
NotesThe comment first proposes an A-Q-Y layout to spread the turrets and reduce the chance that one hit could affect more than one mounting. The answer accepts that a triple mount affects beam and enlarges the protected volume required around shell and powder rooms. A Nelson-like arrangement can partly offset the penalty by putting machinery aft and the main battery and magazines forward. This separation reduces the number of repeated protective and thermal layers needed between engines and ammunition spaces. Supporting facilities can occupy the middle of the hull, creating more distance between the two principal hazards without enlarging every part of the ship proportionally.