¿Hay alguna forma de verificar manualmente qué paquetes adicionales se van a eliminar?

Por ejemplo, supongamos que trato de eliminar "libopenshot11", obtengo:

The following packages will be REMOVED:
  libopenshot11 openshot-qt python3-openshot

¿Cómo puedo encontrar esto sin ejecutar apt remove primero?

La API APT de Python se puede usar para escribir un script corto para esto:

#! /usr/bin/python3
import sys
from apt import cache

c = cache.Cache()
for pkg in sys.argv[1:]:
    c[pkg].mark_delete()   

print('\n'.join(pkg.name for pkg in c.get_changes() if pkg.marked_delete))

Ejemplo:

$ apt-get remove -s bash | grep Remv  
Remv winusb [1.0.11+saucy1]
Remv gdm [3.18.3-0ubuntu2]
Remv gdm3 [3.18.3-0ubuntu2]
Remv bash [4.3-14ubuntu1.2] [inxi:amd64 lightdm:amd64 bash-completion:amd64 ]
Remv bash-completion [1:2.1-4.2ubuntu1.1] [inxi:amd64 lightdm:amd64 ]
Remv inxi [2.2.35-0ubuntu1] [lightdm:amd64 ]
Remv lightdm [1.18.3-0ubuntu1.1]

$ apt-cache rdepends bash --installed | sed '1,2d' | sort -u
  bash-completion
    bash:i386
  gdm3
  inxi
  lightdm
  winusb

$ ./check.py bash                                             
inxi
winusb
gdm
gdm3
bash
lightdm
bash-completion

Puede usar la opción --simulateo -s, que le mostrará lo que APT hará cuando ejecute un comando sin hacer nada, por ejemplo ...

$ sudo apt remove -s file
Reading package lists... Done
Building dependency tree        
Reading state information... Done
The following packages were automatically installed and are no longer required:
  libfile-stripnondeterminism-perl libltdl-dev libmail-sendmail-perl libsys-hostname-long-perl po-debconf
Use 'sudo apt autoremove' to remove them.
The following packages will be REMOVED
  cracklib-runtime debhelper dh-autoreconf dh-strip-nondeterminism file gdebi gdebi-core libtool lintian ubuntu-standard
0 to upgrade, 0 to newly install, 10 to remove and 0 not to upgrade.
Remv cracklib-runtime [2.9.2-3]
Remv dh-autoreconf [13] [debhelper:amd64 ]
Remv debhelper [10.2.2ubuntu1] [dh-strip-nondeterminism:amd64 ]
Remv dh-strip-nondeterminism [0.032-1]
Remv gdebi [0.9.5.7+nmu1]
Remv gdebi-core [0.9.5.7+nmu1]
Remv ubuntu-standard [1.379]
Remv file [1:5.29-3] [lintian:amd64 libtool:amd64 ]
Remv libtool [2.4.6-2] [lintian:amd64 ]
Remv lintian [2.5.50.1]

Podemos ver que eliminar el filepaquete sería una muy mala idea ...

La opción -so --simulatese usa para simular cualquier tarea APT sin ejecutarla realmente.

De las páginas de manual oficiales :

 -s, --simulate, --just-print, --dry-run, --recon, --no-act
       No action; perform a simulation of events that would occur based on
       the current system state but do not actually change the system.
       Locking will be disabled (Debug::NoLocking) so the system state
       could change while apt-get is running. Simulations can also be
       executed by non-root users which might not have read access to all
       apt configuration distorting the simulation. A notice expressing
       this warning is also shown by default for non-root users
       (APT::Get::Show-User-Simulation-Note). Configuration Item:
       APT::Get::Simulate.