Yes? No? Yes/No?
Yes, it means Union. But, interestingly it does not mean so in the Classical Yoga Philosophy, such as the one depicted in Yoga Sutras of Patanjali. Yoga means Union in the Vedanta Philosophy that is extended in Bhakti Yoga, Jnana Yoga and Karma Yoga. Here Union does not mean unification of Body and Mind as described by some modern Yogis. Here it means the unification of Individuality and Universality, whether you take it as Individual Soul and Universal Soul, or as Devotee and the Deity, as Individual Consciousness and Universal Consciousness, etc.
No, it does not mean Union in the classical Yoga Philosophy. In the Classical Yoga Philosophy, it actually means Dis-Union of Individual Soul from the Individual Body-Mind complex. drashtru-drushyayoH sanyogo heya-hetuH. tadabhaavadsanyogaabhaavo haanaM taddrusheH kaivalyaM… Yoga Sutras of Patanjali – Chapter 2. This means that the cause of sorrow in human life is Union of Individual Soul with the Body-Mind-World complex. And, When this Union is absent, liberation is achieved.
Yoga as Union of Mind and Body or Mind plus Body plus Breath or such concepts arise from the need of addressing physical and mental health problems that are more prevalent in the modern world. This definition is interesting, but misleading when associated with the Classical Yoga.