Accessing Time Machine Console Messages
The answer is yes - the logs are available. Either historical or as they occur. 

This is the script I use. The -f argument follows the live Time Machine messages:

#!/bin/sh
#
# show time machine logs
# -f = follow

PRED='subsystem == "com.apple.TimeMachine" AND processImagePath CONTAINS "backupd"'

if [ $# -gt 0 ]; then
    log stream --style syslog --predicate "$PRED" --info 
else
    log show   --style syslog --predicate "$PRED" --info | sed -e 's/ localhost / /' \
         -e 's/ (TimeMachine) / /' \
     -e 's/[[]com.apple.TimeMachine.TMLog/[/' \
     -e 's/\.[0-9][0-9][0-9][0-9][0-9][0-9]\+[0-9][0-9][0-9][0-9] / /'
fi


Note you will need to run this with sudo to access all log data.