No. Rashi did not engage in the study of Kabbalah simply because the mystical work did not yet exist. The same applies to Maimonides as can be seen in the works of Menachem Kellner.
The statement that Rashi was unaware of kabbalistic mysticism should not be mistaken for saying that an authentic Kabbalah did not exist. Authentic Kabbalah existed. We know it must have because Ibn Ezra spoke of Kabbala. But it is not the same Kabbala as promoted today. Kabbala is a body of transmission. Nothing more.
Nachmanides, a mystic also spoke of Kabbala. Although he was very intelligent and a brilliant rabbi, he seemed to have suggested that G-d has "parts," as suggested in the works of the Zohar and Tayna. However, we should note that Nachmanides, being as brilliant as he was, would reject this idea today. He believed it then because he was a product of his time. This argument is supported in an essay by Rabbi Natan Slifkin where he explains that Rashi was a corporealist, but ends his essay with a paradox, "Rashi said it, but we cannot.