I've acted as your post suggest. Before doing that, I've also also used the Anti-theft website to notify this computer is not lost (just in case the emails are being sent daily when no reply from user is detected).
Then I activated the logging, powered off the computer, loggen on (as my password-protected user), disabled logging and then checked my email to make sure there was a new email from Eset Anti-Theft.
Then I used Eset LogCollector to collect logs of almost all.
I'm not very happy about publishing here such complete logs of my computer, since they will