We use our most recent training set for the RICO code to estimate the impact of recombination uncertainties on the posterior probability distributions which will be obtained from future cosmic microwave background experiments, and in particular the Planck satellite. Using a Monte Carlo Markov Chain (MCMC) analysis to sample the posterior distribution of the cosmological parameters, we find that Planck will have biases of -0.7, -0.3 and -0.4σ for nS,Ωbh2 and log(1010AS), respectively, in the minimal six-parameter Λ cold dark matter model, if the description of the recombination history given by RICO is not used. The remaining parameters (e.g. τ or Ωdmh2) are not significantly affected. We also show that the cosmology dependence of the corrections to the recombination history modelled with RICO has a negligible impact on the posterior distributions obtained for the case of the Planck satellite. In practice, this implies that the inclusion of additional corrections to existing recombination codes can be achieved using simple cosmology-independent `fudge functions'. Finally, we also investigated the impact of some recent improvements in the treatment of hydrogen recombination which are still not included in the current version of our training set for RICO, by assuming that the cosmology dependence of those corrections can be neglected. In summary, with our current understanding of the complete recombination process, the expected biases in the cosmological parameters inferred from Planck might be as large as -2.3, -1.7 and -1σ for nS, Ωbh2 and log(1010AS), respectively, if all those corrections are not taken into account. We note that although the list of physical processes that could be of importance for Planck seems to be nearly complete, still some effort has to be put into the validation of the results obtained by the different groups. The new RICO training set as well as the fudge functions used for this paper are publicly available on the RICO webpage.