Convoy demand reduced the destroyers available at Harwich

Did the Harwich Force's destroyer strength fall because convoys needed escorts?

Yes. Convoys competed with several fleets and patrols for a destroyer force whose losses and expanding duties outpaced construction.

The introduction and expansion of convoys drew destroyers from Harwich, the Grand Fleet, the battlecruiser force, and the Dover Patrol. Combat losses reduced the pool at the same time. Shipyards continued building replacements, but the demand for escort and fleet duties grew faster than output. This persistent allocation problem lies behind the refrain that a navy always needs more destroyers.