To be perfectly honest, the fact everyone has phased out any and all traces traditional units irritates me for some reason >.>
Alright, I've been trying to hold back but I got to say something.
They're dead and gone.
Russian or Anglo intervention in China should have and would have saw fit to export modern arms to the warlords of China. Even the warlords furthest from Nanjing - and by that Chiang Kai-Shek and Sun-Yet Sen - could afford to purchase airplanes as far north as Manchuria. There were wide-spread western interests in China due in part to various formal recognition of zones of influence over China with factors like Russia and Britain's Great Game over central Asia, which included areas of China. As a way to extend their influence weapons were often sold en'masse to China in exchange for economic rights or access.
To compound this, the Qing Dynasty had been attempting to implement horribly late-game reforms to salvage their rule. Including purchasing modern weapons to re-arm their armies and modernize their navy. Although being too late for them, this ended pretty badly. As a point: during the Sino-Japanese War, Chinese officers were known to have pawned off the main guns of their destroyers (in addition to sailors storing trash in those guns and all-around terrible maintenance).
So the modern weapons are there, and they'll continue to come in. Even Tibet underwent an incredible degree of westernization under Thubten Gyatso, who chose to build, model, and arm Tibet's own army after the British military. Mongolia as well was receiving support from Russia.
Of course, with the Republic being virtually divided (which OP fails to recognize) between Yuan Shikai's "New Chinese Empire" in Beijing and the actual Chinese Republic in the south; due in part because Yet-Sen lacked the military support Shikai possessed, but all the same divided the Empire.
Yuan Shikai's rule was however just as shaky in the south, but I would imagine Nanjing would have as much influence over the warlords in the south as Shikai in Beijing, since many weapons sales would - and should - be performed by foreign powers through them. As a matter of fact, the meager Republican Navy (which was little more than river boats) was built by Chiang Kai-Shek and Sun Yet-Sen because they were the recognized heads of government in the recognized ROC (more Kai-Shek being the nation's top general, but that's another matter).
But as for Yuan Shikai, if this is set when he declared himself Emperor/President for life then this would more accurately make the RP set in 1915.