Definitely it can be done, as we have evidence that women underwent Upanayana ceremony during the Ramayana period.
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The Emblem
" The wavy waters in the picture are symbolic of Karma, the lotus of Bhakti, and the rising-sun of Jnana. The encircling serpent is indicative of Yoga and awakened Kundalini Shakti, while the swan in the picture stands for Paramatman. Therefore, the ideal of the picture is that by the union of Karma, Jnana, Bhakti and Yoga, the vision of the Paramatman is obtained "~Swami Vivekananda