When GCMs are calibrated do they use 'corrected rainfall' input?
Precipitation is the results of physical processes. As each model implement convective and thermodynamic processes differently (mainly through parametrization or imposed by different grid cell resolution), each model will produce different precipitation. Hence, in other words, you can't tune precipitation, but you can tune the parameters that will produce precipitation. As rainfall is not an easy observable, especially in the period usually used for tuning (~1850-1900), climate modelers does not use such information for their tuning.

Mauritsen et al. (2012) gives an interesting overview of this subject. The abstract is given below. From this article, it states (emphasis are mine) : 

"[...] Formulating and prioritizing our goals is challenging. To us, a global mean temperature in close absolute agreement with observations is of highest priority because it sets the stage for temperature-dependent processes to act. For this, we target the 1850–1880 observed global mean temperature of about 13.7 \deg C [Brohan et al., 2006]. Beyond that, we prioritize having globally averaged TOA shortwave absorption and outgoing longwave radiation in good agreement with satellite observations, along with a representation of important climate variability modes. [...]"

Abstract

"During a development stage global climate models have their properties adjusted or tuned in various ways to best match the known state of the Earth’s climate system. These desired properties are observables, such as the radiation balance at the top of the atmosphere, the global mean temperature, sea ice, clouds and wind fields. The tuning is typically performed by adjusting uncertain, or even non-observable, parameters related to processes not explicitly represented at the model grid resolution. The practice of climate model tuning has seen an increasing level of attention because key model properties, such as climate sensitivity, have been shown to depend on frequently used tuning parameters. Here we provide insights into how climate model tuning is practically done in the case of closing the radiation balance and adjusting the global mean temperature for the Max Planck Institute Earth System Model (MPI-ESM). We demonstrate that considerable ambiguity exists in the choice of parameters,and present and compare three alternatively tuned, yet plausible configurations of the climate model. The impacts of parameter tuning on climate sensitivity was less than anticipated."

Citation

Mauritsen, Thorsten, Bjorn Stevens, Erich Roeckner, Traute Crueger, Monika Esch, Marco Giorgetta, Helmuth Haak, et al. 2012. “Tuning the Climate of a Global Model.” Journal of Advances in Modeling Earth Systems 4 (3): n/a – n/a. doi:10.1029/2012MS000154.