Post-modern technology no way.
It's about supply.
The Chinese had problems fielding troops during the Imjin War because it was just too far from any base of production.
I think there would be a small influence on Chinese culture from the Japanese, but eventually it would become China. Worst case scenario, Hideyoshi becomes Emperor of China, but he loses power, and Japan becomes part of China from then on.
To control China his heirs would have had to live in the capital, as the Manchu did, and thus culturally he would be Chinese and take a Chinese Han bride. His descendants would also be Chinese, and as there would be little distinction between aesthetics, he would have a rightful claim to the Japanese islands.
This was pretty much how Manchuria became part of China. It was abandoned in favor of the greater power and control of the Han capital. Now it is just a smaller province of a Chinese nation.