For a short answer: never.

Well, it seemed that sometimes yes.

We'll compromise: sometimes :)

Undoubtedly, above add_vertex function searches vertex by properties and should return descriptor of found vertex. Indeed, it doesn't.

I'm a little bit confused.

I'm a little confused to. The vertex_by_property call will only actually search the vertices if the adjacency_list is using the named_graph framework. If you're not using - and its almost certain that you aren't - the function call evaluates to a no-op.

I would say that for the most part - it's just a push_back.