Bear in mind that Zen is a form of Buddhism, and as such, has religious and philosophical depth. That being said, as with many such traditions, the point is for a practitioner to directly experience the religious revelations if the practitioner is drawn to the religion. Most sanghas are perfectly happy to teach a secular lay practitioner how to meditate if he/she is open, honest, and respectful regarding intentions. In that case, you won't be given koans (assuming the school of Zen you are visiting uses them) or dharma talks. You'll be taught how to meditate. Just like with mindfulness training, that starts with the counting and experience of the breaths.
Zen employs mindfulness as well as other tools for spiritual cultivation.