Appears not to.
rsyslog writes some files in /var/log/ folder such as:
auth.log
syslog
daemon.log
kern.log
user.log
and so on.

None of the files are available. But rsyslog package exists.

rsyslog is in:
/usr/lib/rsyslog
/UNIONFS/etc/rsyslog.conf
/UNIONFS/etc/rsyslog.d

/usr/bin/rsyslog/rsyslog-rotate

Could the plan be explained please?