No it does not because you can cut out the timestamp and put it into anything if the timestamp doesn't encode anything about the frame contents.
It is always possible to backdate file edits.
Sure, public digital timestamping services exists, but most people will not check. Also once again, an older timestamp can simply be cut out of one file and posted into another file.
You absolutely must embedd something which identifies what the media file is, which can be used to verify ALL of the contents with cryptographic signatures. This may additionally refer to a verifiable timestamp at some timestamping service.