No, Tor does not leak your time zone.
Tor Browser uses UTC for its time. This hides the "system time" from any querying websites and stops any website that could read the time from determining your location based on your timezone.
However it is not able to protect users whose time is uniquely inaccurate. You should use some timesync mechanism to ensure that you keep your system time accurate with reference time, through NTP or similar mechanisms.
From the Tor Browser Design Specification:
Timezone and Clock Offset
While the latency in Tor connections varies anywhere from milliseconds to a few seconds, it is still possible for the remote site to detect large differences between the user's clock and an official reference time source.
Design Goal: All Tor Browser users MUST report the same timezone to websites. Currently, we choose UTC for this purpose, although an equally valid argument could be made for EDT/EST due to the large English-speaking population density (coupled with the fact that we spoof a US English user agent). Additionally, the Tor software should detect if the users clock is significantly divergent from the clocks of the relays that it connects to, and use this to reset the clock values used in Tor Browser to something reasonably accurate. Alternatively, the browser can obtain this clock skew via a mechanism similar to that used in tlsdate.
Implementation Status: We set the timezone using the TZ environment variable, which is supported on all platforms.
While Tor, the network protocol, is agnostic to the data sent over it Tor Browser takes steps to avoid being fingerprintable.