  Flattened and kinematically correlated planes of dwarf satellite galaxies
have been observed in the Local Volume. The slinging out of satellites during
host galaxy mergers has been suggested as a formation mechanism for these
peculiar structures. We statistically examined the impact of major mergers on
present-time satellite systems for the first time in a full cosmological
context using the IllustrisTNG suite of hydrodynamic simulations. Mergers with
mass ratios above 1/3 generally have a negligible or adverse impact on the
phase-space correlation of observationally motivated satellites. Even
high-angular momentum mergers are inefficient at slinging satellites outward
due to the extended nature of simulated satellite distributions. Furthermore,
any potential merger imprint is partially washed out by post-merger accretion
of satellites, while satellites bound to the merging haloes since the merger's
beginning are disrupted and stripped of mass - minimising the merger's
influence on the present-time distribution of the most massive satellites after
2-5 Gyr. Constraining our sample to satellites bound to their host throughout
the full duration of their system's last merger, we recover no particular
improvement in their phase-space correlation. Instead, such participant
satellites experience a contraction of their radial distribution during and
after the merger, resulting in smaller absolute plane heights (but comparable
axis ratios). Overall, major mergers do not appear to form correlated planes in
a statistical sample. Mergers that efficiently transfer their angular momentum
to satellite distributions can marginally enhance their phase-space
correlation, but cannot form highly flattened and orbitally coherent
configurations as observed in our local Universe.
