I'm not exactly familiar with the Zero's hardware. However, the RTC is not a seperate component on the board, but a part of the SAMD21 chip.
Once you configure the RTC to run, it will continue counting while the board is powered up.
If the board resets, the library attempts to preserve the existing clock time. This is contigent on the RTC being configured before the reset event. There is also the option to force it to reset the clock by passing an optional true to the begin() method.
Edit: I have checked the datasheet, and the RTC is reset when the board is power off and then on (Power On Reset).