Based on this, http://forum.parallels.com/showthread.php?t=108231 which is also reproducable on Linux, there is an another bug in PLESK - ATMail.
If a user is like on this topic, without password field, then in ATMail cannot login.
If I switch to HORDE, all is working.
If a user is like on this topic, without password field, then in ATMail cannot login.
If I switch to HORDE, all is working.