нет. По умолчанию непонятно куда оно пишется. Может быть, вообще в память
By default, the journal stores log data in /run/log/journal/. Since /run/ is volatile, log data is lost at reboot. To make the data persistent, it is sufficient to create /var/log/journal/ where systemd-journald will then store the data:
mkdir -p /var/log/journal systemd-tmpfiles --create --prefix /var/log/journal
See journald.conf(5) for information about the configuration of this service.