Yes, but some languages can drop the pronoun in favor of some other linguistic construct. For example in finnish 'I am driving" can be said "minä ajan" but "minä"(I) can be dropped completely to just "ajan" because base word for driving is "ajaa" and when I am doing it, it is inflected to "ajan"
That's also true of Estonian and Spanish, but in the case of "I am he", you'd shorten away the actor, but not the target of the action, so you'd keep one pronoun still at least.