That's just a toy calculation, there's no reason to take the result seriously. The diffusion time is actually more like 170,000 years, and that still doesn't count the time "spent waiting between emissions". If you include that time (which is a lot), you get not the diffusion time, but rather what is known as the "Kelvin-Helmholtz time". The diffusion time is essentially the radiant energy in the Sun at any moment divided by the luminosity of the Sun, and the K-H time is the total energy in the Sun (mostly in hot gas, and much more than in the radiation) divided by the luminosity. The latter is about two orders of magnitude higher than the former.