Would Beatty return in time for Jutland?

Would Beatty make it back from the Mediterranean in time for the Battle of Jutland?

Not necessarily. He might remain in command of Allied naval operations in the Mediterranean, leaving Sturdee or Hood with the battlecruisers.

Beatty might remain occupied by Mediterranean operations rather than return to the Grand Fleet before Jutland. A sufficiently prestigious success could make him the senior commander coordinating British, French, Italian, and Russian naval forces in the theatre. Sturdee or Hood would then be plausible alternatives for command of the British battlecruisers. With Russia under less pressure, Germany might also become more willing to risk a surface-fleet action in search of a strategic change.