It does not. But you may want to look into a free utility to DVDate.
Though one will have to do the "info gathering," one can also just create a Lower-third (or similar) Title and type in the Date/Time. In this case, the time would not be animated, as DVDate's will be. Still, for a general Date/Time it will be very simple.
Even high-end programs, like PrPro and AfterEffects cannot automatically place the Date/Running Time on the Video, though each can add a TimeCode, but that is the running time for the Clip and does not, in any way, relate to when the footage was captured. One must use another program to add that.
You do not want the free DVDate. That will not do what you want to do.
You want the DVDate plugin which has a free demo, but will need to be purchased if you want to use it further
I have been down this road before.
Thanks for that clarification. I have the Russian DVDate that you link to, but have never used it. I also am continually confused as to which DVDate does what, and how.