This paper continues the exploration of \gls{ml} parameterization for radiative transfer for the \gls{icon}. Three \gls{ml} models, developed in Part I of this study, are coupled to \gls{icon}. More specifically, a UNet model and a bidirectional \gls{rnn} with \gls{lstm} are compared against a random forest. The \gls{ml} parameterizations are coupled to the \gls{icon} code that includes OpenACC compiler directives to enable \glspl{gpu} support. The coupling is done through Infero, developed by ECMWF, and PyTorch-Fortran. The most accurate model is the bidirectional \gls{rnn} with physics-informed normalization strategy and heating rate penalty, but the fluxes above 15\,km height are computed with a simplified formula for numerical stability reasons. The presented setup enables stable aquaplanet simulations with \gls{icon} for several weeks at a resolution of about 80\,km and compare well with the physics-based radiative transfer solver ecRad. However, the achieved speed up when using the emulators and the minimum required memory usage relative to the \gls{gpu}-enabled ecRad depend strongly on the \gls{nn} architecture. Future studies may explore physics-constraint emulators that predict heating rates inside the atmospheric model and fluxes at the top.