High Sierra and Outlook 2016 Minimum Version Requirement.

I wish I could remember where I grabbed this from to properly credit it, but we use a script found on jamfNation to register Office 2016 applications with MAU so even if they are not executed by the user they still receive updates

#!/bin/sh

#
# Create MAU trust Launch Agent and the Script using scripting method
#

/bin/cat << 'EOF' > "/Library/LaunchAgents/com.umn.registermau.plist"
<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
<plist version="1.0">
<dict>
     <key>Label</key>
     <string>com.umn.registermau</string>
     <key>ProgramArguments</key>
     <array>
          <string>/usr/local/bin/RegisterMAU.sh</string>
     </array>
     <key>RunAtLoad</key>
     <true/>
</dict>
</plist>
EOF

/bin/cat << 'EOF' > "/usr/local/bin/RegisterMAU.sh"
#!/bin/sh

###############################################################################################################
#
# Register MAU using a Launch Agent (/Library/LaunchAgents/com.umn.registermau.plist)
#
###############################################################################################################

###########
# Functions
###########

# Check if com.umn.MAUtrustDone.plist file exists and if yes don't re-register
checkMAUtrustDone() {
     if [ -f $HOME/Library/Preferences/com.umn.MAUtrustDone.plist ] ; then
        exit 0
    fi
}

# re-register and create a file called com.umn.MAUtrustDone.plist
trustMAU() {
if [ -e "/Library/Application Support/Microsoft/MAU2.0/Microsoft AutoUpdate.app" ]; then
     /System/Library/Frameworks/CoreServices.framework/Frameworks/LaunchServices.framework/Support/lsregister -R -f -trusted "/Library/Application Support/Microsoft/MAU2.0/Microsoft AutoUpdate.app"
fi

if [ -e "/Library/Application Support/Microsoft/MAU2.0/Microsoft AutoUpdate.app/Contents/MacOS/Microsoft AU Daemon.app" ]; then
     /System/Library/Frameworks/CoreServices.framework/Frameworks/LaunchServices.framework/Support/lsregister -R -f -trusted "/Library/Application Support/Microsoft/MAU2.0/Microsoft AutoUpdate.app/Contents/MacOS/Microsoft AU Daemon.app"
fi

# Add office apps to com.microsoft.autoupdate2 plist
# Taken from Office Postinstall script and edited
applications="
Word.app
Excel.app
PowerPoint.app
OneNote.app
Outlook.app"

for application in $applications
do
     domain="com.microsoft.autoupdate2"
     defaults_cmd="/usr/bin/defaults"
     application_info_plist="/Applications/Microsoft $application/Contents/Info.plist"
     lcid="1033"

     if /bin/test -f "$application_info_plist"
     then
          application_bundle_signature=$($defaults_cmd read "$application_info_plist" CFBundleSignature)
          application_bundle_version=$($defaults_cmd read "$application_info_plist" CFBundleVersion)
          application_id=$(printf "%s%02s" "$application_bundle_signature" "${application_bundle_version%%.*}")
          $defaults_cmd write $domain Applications -dict-add "/Applications/Microsoft $application" "{ 'Application ID' = $application_id; LCID = $lcid ; }"
     fi
done

/usr/bin/touch $HOME/Library/Preferences/com.umn.MAUtrustDone.plist
}

# Execute the Functions
checkMAUtrustDone
trustMAU

exit 0
EOF


# Set the correct permissions on the created files
/usr/sbin/chown -R root:wheel "/Library/LaunchAgents/com.umn.registermau.plist"
/bin/chmod -R 644 "/Library/LaunchAgents/com.umn.registermau.plist"

/usr/sbin/chown -R root:wheel "/usr/local/bin/RegisterMAU.sh"
/bin/chmod a+x "/usr/local/bin/RegisterMAU.sh"

# Run Once for current user as LaunchAgent will kick-in for next user onwards and we are running the initial run as root.
CurrentloggedInUser=$(/usr/bin/python -c 'from SystemConfiguration import SCDynamicStoreCopyConsoleUser; import sys; username = (SCDynamicStoreCopyConsoleUser(None, None, None) or [None])[0]; username = [username,""][username in [u"loginwindow", None, u""]]; sys.stdout.write(username + "
");')

if [ -e "/Library/Application Support/Microsoft/MAU2.0/Microsoft AutoUpdate.app" ]; then
     sudo -u "$CurrentloggedInUser" /System/Library/Frameworks/CoreServices.framework/Frameworks/LaunchServices.framework/Support/lsregister -R -f -trusted "/Library/Application Support/Microsoft/MAU2.0/Microsoft AutoUpdate.app"
fi

if [ -e "/Library/Application Support/Microsoft/MAU2.0/Microsoft AutoUpdate.app/Contents/MacOS/Microsoft AU Daemon.app" ]; then
     sudo -u "$CurrentloggedInUser" /System/Library/Frameworks/CoreServices.framework/Frameworks/LaunchServices.framework/Support/lsregister -R -f -trusted "/Library/Application Support/Microsoft/MAU2.0/Microsoft AutoUpdate.app/Contents/MacOS/Microsoft AU Daemon.app"
fi

# Add office apps to com.microsoft.autoupdate2 plist
# Taken from Office Postinstall script and edited
applications="
Word.app
Excel.app
PowerPoint.app
OneNote.app
Outlook.app"

for application in $applications
do
     domain="com.microsoft.autoupdate2"
     defaults_cmd="/usr/bin/sudo -u $CurrentloggedInUser /usr/bin/defaults"
     application_info_plist="/Applications/Microsoft $application/Contents/Info.plist"
     lcid="1033"

     if /bin/test -f "$application_info_plist"
     then
          application_bundle_signature=$($defaults_cmd read "$application_info_plist" CFBundleSignature)
          application_bundle_version=$($defaults_cmd read "$application_info_plist" CFBundleVersion)
          application_id=$(printf "%s%02s" "$application_bundle_signature" "${application_bundle_version%%.*}")
          $defaults_cmd write $domain Applications -dict-add "/Applications/Microsoft $application" "{ 'Application ID' = $application_id; LCID = $lcid ; }"
     fi
done

exit 0

A configuration profile can also be applied to force "Download and Install all Updates" to be the checked option in MAU.

You can also install just the latest Outlook client.

Office 2016 Update History