You might have trouble getting it built though, since it'll presumably be built in the US who is a signature.
Yes and no. The US used some "creative accounting" for the tonnage in their treaty battleships. The official displacement often didn't match the actual displacement. The NorCal Class, which were treaty battleships, displaced 36,600 tons at standard displacement and 44,800 tons at full load when commissioned in 1942. The SoDaks were heavier than the NorCals at standard displacement (38,664) and full load (44,519).
I can probably get away with a heavy ship, and can probably get away with a 16" gun, especially this late in the decade. The BB-3 Class won't commission until 1941.
I did bump up against treaty restrictions with the CA-5 Rio Grande Class. I originally designed them for 10" guns, but no one made a good 10" gun in the late 20's...so I had the US 'impose' the armament size limit on the ship and armed them with 8" guns.
As far as I know, I'm the only country building new battleships in the late 30's that isn't a treaty member (except Germany, who had to contend with the Treaty of Versailles.)