I don't think that is possible. The User Manual only makes reference to adding date stamps to images (see page 33).
If you've already enabled date stamps and are finding that video won't include them, then you'll know it's indeed not possible.
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Ricky
Camera: EOS 5D IV, EF 50mm f/1.2L, EF 135mm f/2L
Lighting: Profoto Lights & Modifiers
