it depends on your tolerance to errors.
In most cases you can compute distances with enough precision when you work in a local projected coordinate system on a "small" regions (for instance, computing the shortest route for a car in a city). Accross China, you are no more in a local projected coordinate system, so the errors could be quite large.
Then, of cours, the geodetic distance (based on Vincenty's formula) is the "reference" distance for shortest path if you go straigth from A to B without obstacles, and it is not "that" slow to compute it with modern computers. But in Distance measurements across UTM zones: use geographic or planar approaches? , you can also see that a sinusoidal projection remains quite good approximation in most cases. And if you have a central point from which all distances are computed, then it would be accurate to use an azimuthal equidistant projection.
Finally, ask yourself what would be the largest source of errors to get the full picture of accuracy, e.g.
planes don't use the shortest distance but have several constraints to take into account, and the most important is the wind
most vehicles don't use the shortest distance but follow the road, rails etc.
if you climb a mountain, the real distance can sometimes be more effected by the slope than the distortions of the 2D projection
