Close. The Sun is not a fully convective star. Convection only occurs in the outer 30% or so. The inner part is called the radiation zone [1] and it is here that energy from fusion in the core makes its way out by radiative transfer as well as conduction. This is a very slow process compared to convection, taking more than 170,000 years for the photos produced by fusion to reach the convection zone.

[1] https://en.wikipedia.org/wiki/Radiation_zone