Okay.... here is my input. I didn't read your description thoroughly enough, and I didn't know that this mentally ill person was making this woman up.
So as I read/listened to the lyric, questions arose.... confusion arose.
THEN.... I figured out that since he's mentally ill, she MIGHT BE imaginary. Figuring it out for myself MADE the song for me.
Only then did I go back and find out that you had already told me that.
My only suggestion is DON'T tell your audience she's imaginary.
Maybe provide some more obvious clues in the lyric, but an audience will almost always appreciate and remember something they figure out themselves better than something they are given.
For me, the song has way more meaning because I figured it out before I realized I had already been told.