A Funny Thing Happened on the Way to the Forum/WMG

The events of the musical were the initial sequences in a Butterfly Effect that eventually brought the Roman Empire to its ruin.
That girl and that boy - the ones with the matching necklaces - will be the ancestors of Pope Leo.
 * "Nothing for kings, nothing for crowns..." That isn't just a description, it's a prophecy!
 * And this musical ends with fun and silliness triumphant. This attitude became infectious until everyone became addicted to the circus.

That really was the Third Doctor in the film; he was just passing through, and decided to meddle a little bit along the way. Pseudolus becomes a new Companion shortly after the film ends.