Yes. Roma does have some troubling New Age/occult connections.
First, she is a graduate from the (unaccredited) University of Santa Monica, a private graduate school founded by New Age self-help guru John-Roger, with a master’s degree in spiritual psychology.
Just for some background, USM founder John-Roger, formerly Roger Delano Hinkins, also founded the Movement of Spiritual Inner Awareness church which utilizes a meditation technique similar to Transcendental Meditation to help people connect with their inner divinity. He changed his name to John-Roger after visiting two trance-channelers who helped him encounter a higher consciousness named "John within himself" and thereafter began referring to himself by John-Roger.
Downey also has a disturbing relationship with John Edward, the famed necromancer (who calls himself a Catholic). According to this article, she appeared on Edward's show on the Sci-Fi Channel and allowed him to contact a spirit who was allegedly her mother, Maureen, who died of a heart attack when Roma was 10. During the session, Roma was told that her mother was proud of the work she was doing.
She also teamed up with Edward to produce a CD on which she recites the Rosary to accompany his book, Practical Praying: Using the Rosary to Enhance Your Life. This is hardly a Catholic concept of the Rosary, but presents it as a "tool to bring focused energy and creative thought into your everyday life." He uses it to show people how to use God's gift of free will - not to surrender to God - but to use it to "chart our own course."
Even more alarming, she also teamed up with Edward to produce a CD for children entitled Loyalty to Your Soul to be used for "meditation and enlightenment". Other contributors to the book include Neale Donald Walsch, author of Conversations with God, books which contain alleged messages from God which are riddled with heresies.
She wrote this glowing endorsement in the beginning of the book which reads:
“As a USM [University of Santa Monica] graduate, I know firsthand the value I received from participating with Ron and Mary in the Master’s degree Program in Spiritual Psychology. I am so grateful to have Loyalty to Your Soul to sweetly remind me of all I have learned. Let’s just say that I went from playing an angel on TV to living more of an angelic life every day. The teachings in this beautiful book have sent me on a journey to the very center of my own being where, wrapped in the safe wings of Love, I feel as though I have come home.”
The answer to your question is yes, Catholics should be concerned about Roma Downey's connection to both the New Age and the occult.