It can be true, but I've found as often as not that work can grow to fill your time like a gas. No matter how much of it you can automate away, it simply means you can do more stuff.
A programmer will automate some tedious repetitive task, and then boast about the automation to his programmer peers and managers. The programmer will then be rewarded with more tedious tasks to deal with.
A sysadmin automates a boring task, and tells nobody. The only way anyone can request work done is to file a ticket in the ticket tracker. The work gets done, but nobody besides the sysadmin knows how it was done. If the sysadmin is good at his job, he is rarely seen at his desk, and often seen playing foosball.
If you can replace someone's job with the proverbial small shell script (or apt-get install $OPENSOURCEPROJECT), sooner or later that is what will happen.