Your right about this Ledo road:
The Ledo Road (from Ledo, Assam, India to Kunming, Yunnan, China) was built during World War II so that the Western Allies could supply the Chinese as an alternative to the Burma Road which had been cut by the Japanese in 1942. It was renamed the Stilwell Road (named after General Joseph Stilwell of the U.S. Army) in early 1945 at the suggestion of Chiang Kai-shek. It passes through the Burmese towns of Shingbwiyang, Myitkyina and Bhamo in Kachin state.
One interesting fact about land road is that it cannot compete with the airways:
As General Chennault had predicted, supplies carried over the Ledo Road at no time approached tonnage levels of supplies airlifted monthly into China over the Hump. In July 1945, the last full month before the end of the war, 71,000 tons of supplies were flown over the Hump, compared to only 6,000 tons using the Ledo Road; the airlift operation continued in operation until the end of the war, with a total tonnage of 650,000 tons compared to 147,000 for the Ledo Road. By the time supplies were flowing over the Ledo Road in large quantities, operations in other theaters had shaped the course of the war against Japan.
http://military.wikia.com/wiki/Ledo_Road
So, from gameplay POV, when Axis is owning a given TT from the Burma road, it is a way of acknowledging that airlift transports are no more possible over a given portion of Burma Road. (Too much AA guns… and too long flight.)
Also, Kunming in Yunnan was the delivery point, but it does not mean the material is given to Chinese soldiers and divisions. Hence, the addition of Chungking in Szechwan, as the capital-in-exile of Republic of China, where we presume are the training grounds and division camps to built their armies.