It depends upon your definition of "off", "track", and "phone".
Some phones will keep the baseband chip powered when the device has been shut down. In some cases, security agencies have "updated" the baseband sofware on a large number of phones in order to make them trackable when shut down. It's certainly possible to install OTA updates with almost unlimited abilities on most modern phones, though you would require co-operation from a network, or possibly to run a rogue cell tower.
From an article in Slate:
In 2006, it was reported that the FBI had deployed spyware to infect suspects’ mobile phones and record data even when they were turned off... In 2009, thousands of BlackBerry users in the United Arab Emirates were targeted with spyware that was disguised as a legitimate update. The update drained users’ batteries and was eventually exposed by researchers, who identified that it had apparently been designed by U.S. firm SS8, which sells “lawful interception” tools to help governments conduct surveillance of communications.
With reference to the above article:
According to Gallagher, the NSA may be using mass updates to infect phones of targets overseas (and presumably, any "non-targets" applying the same faux update). This would be difficult, but not impossible, and considering what we've learned about the NSA's far-reaching surveillance net, certainly not implausible.
In summary, the answer is Yes, at least some phones, when they appear to be off, could connecting to a cell tower, and could be tracked to some extent. Given that this article is covering a story from the Washington Post, this is a credible claim.