Battlecruisers do not require fewer turrets

Would the G3 need one fewer turret to qualify as a battlecruiser?

No. Reduced turret counts resulted from machinery and speed tradeoffs, not from a categorical requirement for battlecruisers.

Some battlecruisers lost a turret because their designers needed hull volume and weight for more machinery. That was an engineering consequence of buying speed, not a rule defining the type. Hood shows that a battlecruiser could retain a battleship-scale turret count. Early dreadnought layouts could also deliver similar effective broadsides despite differing total turret numbers, so broadside strength is more informative than simply counting turrets.