I would say no by contradiction. Let's assume black could win without zugzwang. Then white would win (and in particular not lose) by skipping the very first move and then playing blacks strategy (because now black has to make the first move and by white skipping the first move, the colors swapped).

If white would not skip the very first move and play an arbitrary move instead, white loses and black wins.

But this is the very definition of zugzwang! Thus, black can only win because of white's initial zugzwang, which contradicts our assumption.