Can gutters be installed on top of shingles?
Sometimes the stars align and answers are provided.
After i posted my comment this morning I was watching a previous episode of This old house in which they are restoring a  New England  Victorian house that is regulated by the local historic commission. One of the requirements needed to be met was the restoration of the   Yankee Gutters.
A web search led me to oldhouseguy.com where i found an article about gutters of all kinds including Yankee gutters for old houses.
More about Yankee Gutters at InspectAPedia.
More than you want to know about the history of gutters.
 Credit oldhouseguy.com