I agree with most of the posters here; let the GF sink a few more HSF vessels and nothing really changes. In the OTL, the Germans won a tactical victory of sorts but the strategic picture never changed. Besides, the tactical victory they won was 'Getting away mostly safe from under the guns of a larger fleet'. Nothing to really brag about there. "Phew, we got away..."
Sure, Kaiser Bill and a few other spin doctors thought the entire affair was a great German victory. Scheer, Hipper, their officers, and their crews knew better however. Upon returning to Scapa, Jellicoe wired the Admiralty that the GF would be ready to sortie again in 48 hours. Hipper told his superiors it would be months before the HSF could sortie in full strength again. One author described the entire Jutland episode as the HSF breaking out of jail, punching their GF jailer in the eye, and then being returned to their cell. That pretty much sums it up.
A 'no doubt about it' HSF defeat; one that even Kasier Bill and his fellow loonies couldn't conflate into a German 'victory', may strengthen the hand of the Unrestricted Submarine Warfare lobby. That, in turn, may actually help the Germans. The Germans would begin such operations sooner, support them more fully, and see a much greater effect. By starting earlier, they may have even been able to 'starve out' Britain before the US involved itself.
Why do I believe that to be probable? Two reasons; first, why the US really went to war, and second, the British Admiralty.
Busting a myth here, unrestricted submarine warfare did not bring the US in on the side of the Allies. To be sure, it did lay the groundwork but Wilson did relatively little in the way of preparing the US for war during any of the various sinking crisis; i.e. Lusitania, Arabic, Laconia, etc. He realized that the Midwest and West viewed those sinkings much differently than the East did.
What actually drove the US to war was the Zimmerman Telegram. The prospect of an Imperial Geman-Mexico-Japan alliance (however silly) brought home the idea of war to the relatively isolated Midwest and West. Suddenly, they began to take notice of everything else. IMHO, the Germans could have gone on sinking merchant ships with Americans aboard without the slightest fear of US intervention as only one section of the US; the Eastern Seaboard, viewed such actions with alarm.
The British Admiralty during most of WW1 was... well, dysfunctional is a kind word for it. Despite having numerical superiority, despite reading their enemy's message traffic, and despite having total freedom of the seas while their enemy remained bottled up in harbor, the RN did bugger all during most of the war. There are a lot of reasons for this and most of them can be laid at the feet of institutional inertia. Simply put, neither the system or the men in it were up to the task at hand.
Churchill brought back Fisher early in the war and was repaid by watching Fisher sink quickly into senile dementia under the strain. By the time of the Lusitania affair, Fisher's trolley was nearly completely off the tracks and it could no longer be ignored thaks to his messages to Asquith. Besides saddling the organization with a senile Fisher, Churchill was also a micromanager who routinely involved himself in the most trivial of tasks. This stifled the initiative of those staffers who should have been handling the work in the first place. Churchill wasn't alone in this sin. VADM Henry Oliver, the chief of the Naval War Staff, was a notorious micromanager too. The amount of work, trivial and substantive, that needed to cross his desk prior to it being acted upon was beggars disbelief. Like Churchill, Oliver's work habits stifled the initiative of his underlings and had far reaching consequences(1).
The Admiralty as a whole was slow to act, slow to respond, and slow to show any kind initiative. In 1917 and in the face of a growing submarine threat, convoying even had to be rammed down their collective throats by the politicians. An earlier German push may have had more time to work before the Admiralty was prodded into taking action. Especially if the Admiralty had a 'no doubt about it' victory at Jutland to point to.
So, IMHO, a Jutland deeat could plausibly help the Germans.
Bill
1 - One example of this occurred during the Dogger Bank battle. Beatty; who wasn't very good himself, made a snap decision regarding a reported periscope sighting that allowed the German's to escape. Oliver, thanks to Blinker Hall and the Room 40 code breakers, knew there wasn't a German sub within 50 miles of the action but had failed to pass that information along the Beatty. No one else on the Naval War Staff even thought of telling Beatty either because that was something only VADM Oliver could do.
2 - BTW, the HSF did sortie after Jutland. Many times as a matter of fact, but just not that far north. One such sortie occurred in 1918 while the USN squadron attached to the GF was taking it's turn covering the Scandinvian convoy. A few hours steaming could have seen a HSF-USN battle and one that the USN would not have enjoyed.