Would the High Seas Fleet still come out?

Would the Germans still dare to bring the High Seas Fleet out against the stronger British force?

Probably at first, but not after losing the First Scouting Group that made German raids and traps possible.

Germany would probably keep trying limited operations while its battlecruiser scouting force remained available. The plan assumed that British forces would respond aggressively enough to be drawn onto a prepared fleet. When Britain declined to cooperate, the operational concept already struggled. Destruction of the First Scouting Group at Dogger Bank would remove the raiding and scouting instrument needed to make later traps credible, making continued major sorties far less likely.