Can Horizontal Radiation Fluxes Contribute to Net Column Heating?

I’ve noticed that in many papers it’s common to assume the (daily or longer averaged) vertically integrated radiative heating can be expressed $F_z(text{TOA})-F_z(text{SURF})$, where $F_z$ is the vertical component of radiative flux, and $text{TOA}$ and $text{SURF}$ denote the top of atmosphere and surface respectively, with "top of atmosphere" usually either taken as $zto infty$, or as the tropopause height, depending on the context.

I assume this basically reflects the fact that if we express radiative heating $Q$ as a flux divergence $Q=nabla cdot (F_x,F_y,F_z)$, vertical integration gives
begin{align}
int_text{SURF}^text{TOA} Q ,dz &= int_text{SURF}^text{TOA} nabla_H cdot (F_x, F_y) ,dz + int_text{SURF}^text{TOA} frac{partial F_z}{partial z} ,dz \
&= int_text{SURF}^text{TOA} nabla_H cdot (F_x, F_y) ,dz + F_z(text{TOA})-F_z(text{SURF}).
end{align}

It seems natural to assume the $int_text{SURF}^text{TOA} nabla_H cdot (F_x, F_y) ,dz$ term, which is the net horizontal flux divergence out of the column, will be small compared to the $F_z(text{TOA})-F_z(text{SURF})$ term, but does anyone know just how much smaller? What are some reasonable scale estimates for these terms? Are there situations in atmospheric science where net horizontal radiative flux divergence can’t be neglected?

For example, I’m imagining a column with a single spherical cloud in it, and the sun directly overhead, but no clouds in any other nearby columns. In such a situation, wouldn’t there be a horizontal radiative flux divergence, i.e. a net horizontal radiative flux out of the column? Would this effect still have a negligible impact on net column heating, or does nothing like this occur in real atmospheres?