Yes it does for 23.976Hz, but not for the rare, even 24.00Hz sources.
I respectfully disagree, I like my sources being playbacked with their native refresh rate.
Cinema movies are shot at 23.976fps which is known as 24p. Exception are UK movies shot at 24.000fps and Kodi interpretation is the same for both. It will switch (should) your TV to 24Hz. It does in my case. I checked it like minute ago.
If it doesn't on your setup make adjustrefreshrate overrides in advancedsettings.xml (advancedsettings.xml - Official Kodi Wiki).
The downside of 24Hz if flickering which is more or less visible in some scenes. Especially bright.
Not even cinemas really show 24fps. The shutter rotates so actually you are watching at 48Hz or 72Hz.
More Hz = less flickering.
So if don't wanna hurt your eyes buy a 48Hz, 72Hz or 120Hz panel TV.
I personally like to set 50Hz and let Kodi to match the rest. Basically it's played like PAL standard (all Europe) and it's smooooth And no flickering!