Perhaps. However, if you want to address her as Millie or Milly, why not name her that? We wanted to name our daughter Elizabeth, so that is what we generally address her as. (I also refer to her as Lizzie Bear, Sweet Lizzie, Sweet Lizzie Bear, Baby Bear... but only on occasion and not really in substitution of her name. Generally, it's in comforting or loving terms, like when she is unhappy and we're snuggling, or we're snuggling down for a nursing...)
I guess this comes from the fact that my husband wasn named Darin Andrew, but his mother started to address him as Andy. My parents named me Laura, but addressed me as Lori, until I was 16 and decided that Laura sounded more grownup.