Hmm... I dunno. It makes sense that it was a story about Mary Magdaline that got her thinking along these lines, but it's not possible that she was praying to such a person. She's praying to the Virgin Mary in the song, known in Japanese Catholicism as "Maria" just as in Spanish and Portugese culture.
In my experience, the Virgin Mary is seen in Japan by non-Catholics and perhaps some Catholics as a deity of mercy. Popular culture associates her with love, though this is likely not the intention of any Japanese Catholic. I remember reading an article about Ayu's thoughts on the song and said something like she had regarded Mary as some holy person but then understood that she was a person as well.
Okui Masami sang a song called Maria some years ago on her album Her-Day and it mentioned "cross" and "love" as concepts along with a song-prayer to the Virgin Mary. Ayu's seems very much in line with this song as well. I think that she is seen as a deity of mercy by people in love. I could be wrong, but in my experience, this is the feeling I get.
The translators at Centigrade-J (
http://centigrade.blandplanet.com/) said this on the song in their translation notes:
MARIA is the Christian Religion Holy Mother of Christ. The whole song is a prayer to MARIA to help Ayu find everlasting love in a world where that doesn't seem possible.