Long term, it's probably true that the effect will be a wash.
The typical cycle of automation is that there's some kind of crunch (bad economy, rising wages, etc.) which causes businesses to streamline, including adopting automation.
However, managers are lazy like everybody else, and continually keeping their operations lean & mean would take sustained effort, so head counts creep up again.
When the economy eventually expands (it will, sooner or later), businesses hire even more. They don't automate then because a) automation requires making an investment, yet they can't be sure that the good times will last so it's safer to hire someone who can be easily fired, and b) automating takes management time & effort, plus productivity typically takes a short-term hit, neither of which is acceptable during an expansion phase, i.e. "can't you see we're busy making money now?" In management-speak: staffing up is more flexible and less disruptive than automation.
Wash, rinse & repeat.