"No WT TL" can mean many things, from basically the same political/economical situation, just without the treaty, to the real PoD being drastically changed political/economical conditions making the treaty superflous/impossible.
The first scenario will probably mean more of the planned ships being completed, at least in USA and GB, but rather than a formal treaty setting the limit the powers will anxiously watch each other and not build more than prestige and basic security considerations demands.
France and Italy in OTL build less than the treaty allowed, they simply didn't have neither the money - nor the needs. I very much doubt if Japan will be capable of finishing anything close to the imagined 8-8 programe, certainly not with the 1923 earthquake in place. From the Russo-Japanese War Japan really was broke and politically in chaos well into the 1930's, when something similar to fascists took over and utilised every drop for military purposes.
As others have already said GB wasn't anywhere near broke after WWI, but there was a great wish to take home the peace dividend (= taxreductions and social reforms). Had there been obvious threats to the Empire (like an openly hostile USA or Japan) I'm sure funding for even huge naval programmes would be found. In a TL without significant pol/ec PoD's I guess that at least the G3's would be completed, but the N3's would await what the other powers would do. The British have the advantage of being at least one step ahead in design at this time, and in having a well balanced fleet with a well defined strategic role (defending the Empire - strategic defence).
USA no doubt had the greatest economical resources but in many ways was caught on the wrong leg with the huge naval programme under way in 1922. The designs were extemporations on designs that had been revolutionary before WWI (Nevada - Standard), but by 1922 were obsolescent. Next the USN was unbalanced and especially needed good cruisers to scout, and finally there really wasn't a clearly defined strategic role for the USN. If the task just was defending US coastlines a much smaller and less expensive navy could do it, and by 1920's USA didn't have anything resembling an Empire needing a huge navy to keep it together. But one factor must not be overlooked when talking battleships and that is the prestige and symbolism linked to these giants. By 1920's USA had over the last couple of decades grown a huge self-awareness as a rising great power - but by early 20th century that wouldn't give any meaning without battleships. That explains why the USN was so battleship heavy and why landpowers like Germany and A-H spent huge sums on battleship navies. No matter how stupid or superflous those battleships would be in the strategic situation of those countries they really weren't left with any choice - great power status simply required BB's - but compared to Germany and A-H USA at least had abundant resources and didn't neigbour a huge landpower.
Without a WT I guess most of the ships already on the slips (Colorado, Lexington and South Dakota classes) would have been completed, and that would have satisfied the prestige considerations, but funding for new ships would have been extremely difficult after that - until an obviously dangerous enemy shows up (and then it may be too late). But completing all these ships inside a few years probably also gives the British the necessary legitemacy and funding for going ahead with the N3 programmes, unless they are smart enough to just continue the G3 programme.
The very interesting point is however if a continued naval construction race in the 1920's would have prevented or at least lessened the later crisis. That crisis in many ways was severey reinforced because governments tried to save their ways out of it, but thus only slowed down the wheels by cutting demand. In this context naval construction of some extent would simply have circulated a lot of money creating demand - in short a basic Keynesian cure - which was developed for exactly this situation (of a "understimulated" demand).
I'm sure there could be found more effective or direct methods than building battleships, but at least the battleships look great.
BTW regarding the technical development cost will soon put limits on battleship size. It will become inceasingly clear that even 50, 60 or 70.000 ton giants will be vulnerable and navies will start to look for more cost-effective ways of sinking ships - so no way to avoid torpedoes, subs, mines and aircraft...
Regards
Steffen Redbeard
