Gertie fits in with the nickname trend for sure, but it still seems clunky and awkward to me. It doesn't have a softer part to compensate like the names that have exploded onto the scene do. I think Gertrude itself has the ugly cute vintage vibe going that makes it usable, though a little less so than say Agnes or Edith, and Trudy definitely does.
I don't like Gertie as a full name, but I think Hattie and Callie work, so no reason why not.
~Anna~