The objects are actually defined in the ActivityStreams spec, which is a prereq for ActivityPub. So, a purely static site can only meaningfully implement the former, not the latter. However implementing ActivityStreams object types would still be useful inasmuch as it might provide some limited interop with the Fediverse.

(Future server-side improvements might also allow for some kind of automated polling of statically-hosted ActivityStreams, outside of the standardized "push" model.)