  $Context$. 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-Zel'dovich (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)
