Would battlecruisers strengthen the Harwich Force?

Would assigning the Third Battlecruiser Squadron to Harwich Force improve its operations?

It would add cover, but the accompanying senior admiral could override Tyrwhitt and reduce the force's operational advantage.

Attaching a battlecruiser squadron would give Harwich Force heavy cover against German capital ships. The attachment also arrives with a rear admiral who is unlikely to defer to Commodore Reginald Tyrwhitt, the officer already experienced in the force's operations. That seniority problem could change planning and tactical decisions even when the added ships never fire. Dogger Bank illustrates the institutional cost: Harwich light forces contribute to the battle, but the senior battlecruiser commander controls the action. Reinforcement can weaken a formation when it displaces the command relationship that made the formation effective.