Verified with 1.1ubuntu1.18.04.10 on Bionic:

...
root@bb-uu-lp-1795696-verify:~# eatmydata apt install linux-image-unsigned-4.18.0-13-generic linux-image-unsigned-4.18.0-14-generic linux-image-unsigned-4.18.0-15-generic
...
root@bb-uu-lp-1795696-verify:~# apt-mark auto linux-image-unsigned-4.18.0-13-generic linux-image-unsigned-4.18.0-14-generic linux-image-unsigned-4.18.0-15-generic
linux-image-unsigned-4.18.0-13-generic set to automatically installed.
linux-image-unsigned-4.18.0-14-generic set to automatically installed.
linux-image-unsigned-4.18.0-15-generic set to automatically installed.
root@bb-uu-lp-1795696-verify:~# /etc/kernel/postinst.d/apt-auto-removal
root@bb-uu-lp-1795696-verify:~# apt autoremove 
Reading package lists... Done
Building dependency tree       
Reading state information... Done
The following packages will be REMOVED:
  grub-common grub-gfxpayload-lists grub-pc grub-pc-bin grub2-common libfreetype6 linux-image-unsigned-4.18.0-13-generic linux-image-unsigned-4.18.0-14-generic
  linux-image-unsigned-4.18.0-15-generic linux-modules-4.18.0-13-generic linux-modules-4.18.0-14-generic linux-modules-4.18.0-15-generic os-prober
0 upgraded, 0 newly installed, 13 to remove and 7 not upgraded.
After this operation, 239 MB disk space will be freed.
Do you want to continue? [Y/n] n
Abort.
root@bb-uu-lp-1795696-verify:~# vi /etc/apt/apt.conf.d/50unattended-upgrades 
root@bb-uu-lp-1795696-verify:~# grep Minimal /etc/apt/apt.conf.d/50unattended-upgrades
Unattended-Upgrade::MinimalSteps "false";
root@bb-uu-lp-1795696-verify:~# unattended-upgrade --dry-run --verbose
Initial blacklisted packages: 
Initial whitelisted packages: 
Starting unattended upgrades script
Allowed origins are: o=Ubuntu,a=bionic, o=Ubuntu,a=bionic-security, o=UbuntuESM,a=bionic
Removing unused kernel packages: linux-modules-4.18.0-13-generic linux-modules-4.18.0-15-generic linux-modules-4.18.0-14-generic
Keeping 3 auto-removable package(s) because it would also remove the following packages which should be kept in this step: libntfs-3g88 linux-image-unsigned-4.18.0-13-generic linux-image-unsigned-4.18.0-14-generic linux-image-unsigned-4.18.0-15-generic ntfs-3g snapd
Traceback (most recent call last):
  File "/usr/bin/unattended-upgrade", line 1998, in <module>
    sys.exit(main(options))
  File "/usr/bin/unattended-upgrade", line 1798, in main
    options.verbose or options.debug, options.dry_run)
  File "/usr/bin/unattended-upgrade", line 1495, in do_auto_remove
    if res:
UnboundLocalError: local variable 'res' referenced before assignment
oot@bb-uu-lp-1795696-verify:~# echo "deb http://archive.ubuntu.com/ubuntu/ bionic-proposed restricted main multiverse universe" > /etc/apt/sources.list.d/proposed.list
root@bb-uu-lp-1795696-verify:~# apt update -qq
33 packages can be upgraded. Run 'apt list --upgradable' to see them.
root@bb-uu-lp-1795696-verify:~# apt install unattended-upgrades 
Reading package lists... Done
Building dependency tree       
Reading state information... Done
The following packages were automatically installed and are no longer required:
  grub-common grub-gfxpayload-lists grub-pc grub-pc-bin grub2-common libfreetype6 linux-image-unsigned-4.18.0-13-generic linux-image-unsigned-4.18.0-14-generic
  linux-image-unsigned-4.18.0-15-generic linux-modules-4.18.0-13-generic linux-modules-4.18.0-14-generic linux-modules-4.18.0-15-generic os-prober
Use 'apt autoremove' to remove them.
Suggested packages:
  bsd-mailx default-mta | mail-transport-agent needrestart
The following packages will be upgraded:
  unattended-upgrades
1 upgraded, 0 newly installed, 0 to remove and 32 not upgraded.
Need to get 40.4 kB of archives.
After this operation, 4096 B of additional disk space will be used.
Get:1 http://archive.ubuntu.com/ubuntu bionic-proposed/main amd64 unattended-upgrades all 1.1ubuntu1.18.04.10 [40.4 kB]
Fetched 40.4 kB in 0s (204 kB/s)            
N: Ignoring file 'proposed' in directory '/etc/apt/sources.list.d/' as it has no filename extension
Preconfiguring packages ...
(Reading database ... 32894 files and directories currently installed.)
Preparing to unpack .../unattended-upgrades_1.1ubuntu1.18.04.10_all.deb ...
Unpacking unattended-upgrades (1.1ubuntu1.18.04.10) over (1.1ubuntu1.18.04.9) ...
Processing triggers for ureadahead (0.100.0-20) ...
Processing triggers for systemd (237-3ubuntu10.15) ...
Setting up unattended-upgrades (1.1ubuntu1.18.04.10) ...
Processing triggers for man-db (2.8.3-2ubuntu0.1) ...
N: Ignoring file 'proposed' in directory '/etc/apt/sources.list.d/' as it has no filename extension
root@bb-uu-lp-1795696-verify:~# unattended-upgrade --dry-run --verbose
Initial blacklisted packages: 
Initial whitelisted packages: 
Starting unattended upgrades script
Allowed origins are: o=Ubuntu,a=bionic, o=Ubuntu,a=bionic-security, o=UbuntuESM,a=bionic
Removing unused kernel packages: linux-modules-4.18.0-13-generic linux-modules-4.18.0-15-generic linux-modules-4.18.0-14-generic
Keeping 3 auto-removable package(s) because it would also remove the following packages which should be kept in this step: libntfs-3g88 linux-image-unsigned-4.18.0-13-generic linux-image-unsigned-4.18.0-14-generic linux-image-unsigned-4.18.0-15-generic ntfs-3g snapd
Packages that were successfully auto-removed: 
Packages that are kept back: 
Option --dry-run given, *not* performing real actions
Packages that will be upgraded: libntfs-3g88 ntfs-3g snapd
Writing dpkg log to /var/log/unattended-upgrades/unattended-upgrades-dpkg.log
All upgrades installed
root@bb-uu-lp-1795696-verify:~# unattended-upgrade  --verbose
Initial blacklisted packages: 
Initial whitelisted packages: 
Starting unattended upgrades script
Allowed origins are: o=Ubuntu,a=bionic, o=Ubuntu,a=bionic-security, o=UbuntuESM,a=bionic
Removing unused kernel packages: linux-modules-4.18.0-15-generic linux-modules-4.18.0-14-generic linux-modules-4.18.0-13-generic
Keeping 3 auto-removable package(s) because it would also remove the following packages which should be kept in this step: libntfs-3g88 linux-image-unsigned-4.18.0-13-generic linux-image-unsigned-4.18.0-14-generic linux-image-unsigned-4.18.0-15-generic ntfs-3g snapd
Packages that were successfully auto-removed: 
Packages that are kept back: 
Packages that will be upgraded: libntfs-3g88 ntfs-3g snapd
Writing dpkg log to /var/log/unattended-upgrades/unattended-upgrades-dpkg.log
All upgrades installed
root@bb-uu-lp-1795696-verify:~# 

The unsigned kernels are kept back due to LP: #1821640 .