$Context$. The mean pressure profile of the galaxy cluster population plays an essential role in cosmological analyses. An accurate characterization of the shape, intrinsic scatter, and redshift evolution of this profile is necessary to estimate some of the biases and systematic effects that currently prevent cosmological analyses based on thermal Sunyaev-Zeldovich (tSZ) surveys from obtaining precise and unbiased cosmological constraints. This is one of the main goals of the ongoing NIKA2 SZ large program, which aims at mapping the tSZ signal of a representative cluster sample selected from the $Planck$ and ACT catalogs and spans a redshift range $0.5 < z < 0.9$. $Aims$. To estimate the impact of intracluster medium (ICM) disturbances that can be detected by NIKA2 on the mean pressure profile of galaxy clusters, we realized a study based on a synthetic cluster sample that is similar to that of the NIKA2 SZ large program. $Methods$. To reach this goal we employed the hydrodynamical simulation $Marenostrum~MUltidark~SImulations~of~galaxy~Clusters$ (MUSIC). We simulated realistic NIKA2 and $Planck$ tSZ observations, which were jointly analyzed to estimate the ICM pressure profile of each cluster. A comparison of the deprojected profiles with the true radial profiles directly extracted from the MUSIC simulation allowed us to validate the NIKA2 tSZ pipeline and to study the impact of ICM disturbances on the characterization of the ICM pressure distribution even at high redshift. After normalizing each profile by the integrated quantities estimated under the hydrostatic equilibrium hypothesis, we evaluated the mean pressure profile of the twin sample and show that it is compatible with that extracted directly from the MUSIC simulation in the scale range that can be recovered by NIKA2. We studied the impact of cluster dynamical state on both its shape and associated scatter. (abridged)
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