How do I check that a user password is locked?

You can use the passwd utility to look at the status of the user's password entry

passwd -S user
user LK 2012-11-06 0 99999 7 -1 (Password locked.) (CentOS)
user L 01/22/2013 0 99999 7 -1 (Ubuntu)

The LK as well as the (Password Locked) text indicate a locked password entry on CentOS and L indicates a locked password entry on Ubuntu.

You can also use getent to read the shadow database

getent shadow user
user:!$6$ic7iX.Q2$q9K5gi5pOb...TJlhAIoKVJfAybADtv80:15650:0:99999:7:::

or you can just look at the shadow file yourself

grep user /etc/shadow
user:!$6$ic7iX.Q2$q9K5gi5pOb...TJlhAIoKVJfAybADtv80:15650:0:99999:7:::