An interesting permutation here would be regarding the Washington Naval Treaty. Yes, I do think it's still quite possible - if not very probable - for it to not be butterflied away entirely. The war seems like it might end in early 1917, but even so, the major combatants have spent billions on the war, and lost millions on the battlefield. Britain, despite likely facing instability in her colonies and in Ireland as a result of having to come to terms with the Germans, isn't so beaten that they won't hold onto their status as the world's preeminent naval power, something lampshaded by how Germany's terms for a ceasefire were very much a case of quid pro quo, and explicitly mentioned as born of Germany recognizing and respecting Britain's enduring naval and industrial strength. That said, the rise of Germany as a truly global power as a result of the war, plus Tirpitz ironically being vindicated in how Germany's naval weakness allowed Britain to so easily undermine the German economy, will only mean Germany will look upon the Kaiser's naval ambitions with renewed interest.
On the other side of the Atlantic, the USA despite not having been shocked out of its isolationist stance by joining the war ITTL, has nevertheless seen how its ability to trade with foreign nations is very much at risk at war, whether it's Britain's distant blockade or Germany's U-Boat campaign. And there's the growing might of Japan in the Pacific, especially since it's likely Japan will get to keep Qingdao and the Pacific Islands in exchange for a token, face-saving payment to Germany. Similarly, Japan fears American expansion into the Pacific, and will likely still push for their 8-8 Fleet to deter American attempts to directly threaten them.
Elsewhere, the Mediterranean CPs also recognize the value of naval strength. Even as fleets-in-being, the Regia Marina and the Royal and Imperial Navy together managed to secure their home waters in the Adriatic and Tyrrhenian Seas from the British Mediterranean Fleet and Marine Nationale both. Italy is even mentioned as partly able to weather the British blockade thanks to the Entente's inability to project power into their home waters, as it allowed the fishing industry to operate unmolested.
That said, a naval arms race is not exactly anyone would want. Britain, as I mentioned, will be facing instability in its colonies and in Ireland over her preeminent role as the global hegemon shaken and tarnished by Germany forcing her to the bargaining table. Germany will be busy building up its satellites in Eastern Europe, and with the rest of the CP (and including German-leaning neutrals like Denmark, possibly Sweden and the Netherlands, maybe even a defanged - Grand Duchy of Flanders (?) - Belgium) also building up the new Mitteleuropa order to truly engage in an arms race. Japan will still have to face the Great Kanto Earthquake (virtually impossible for it to be butterflied), and the fact that the IJN's naval ambitions are draining IIRC over 20% of Japan's GDP at the time. Similarly, the US Congress will be balk at attempts to build a fleet greater than Britain's, i.e. "a fleet second to none". This leads us back to Britain, who'll find maintaining a two-power standard against the USN and KM backbreaking for their national expenditures.
So yes, I do think a WNT analog is very likely to come into existence. I also think the butterflies with regard to its details to go in one of two directions. Germany is unlikely to accept a place in the treaty system that lumps it in the third category. Also, Germany - well, Tirpitz and the rest of the naval lobby - may also not accept a 60% ratio to the Royal Navy even if they join Japan in the second category, assuming an OTL tonnage allocation of 5-3-1.75. This leads to a) Germany joining Britain and the USA in the first category, which would be unacceptable to Britain, or b) Germany stays in the second category, but with a different tonnage allocation of 3-2-1. This would be more acceptable to Britain, though less so the USA.
With that ratio though, it's likely for Britain and the USA to keep 15 battleships each, plus two of (theoretically) demilitarized training ships. Japan and Germany would each keep 10 battleships, and the other Great Powers 5 battleships each, plus 1 each of a (again, theoretically) demilitarized training ship.
EDIT: The Americans are still likely to pressure Britain into ending the Anglo-Japanese Alliance in 1923, which would lead to Germany snapping Japan up as an ally. If nothing else, the powerful IJN would serve Germany and Mitteleuropa well in a future war against Britain by tying down large elements of the Royal Navy in the Pacific, and limit the amount of help the ANZACs can send to Europe and elsewhere.
This may also have the effect of limiting/moderating Japanese militarism, as Japan wouldn't be diplomatically-isolated the way she was in the decades between WWI and WWII IOTL, and instead have ties with Germany and Mitteleuropa.