Answer:
I doubt it. Savannah was born 1971, daughter of the late charlie Guthrie, an engineer (Charley was once my Sunday School teacher,) and of Nancy Guthrie, a writer.
Savannah spent her formative years and early career in Tucson. I never heard that Arlo Guthrie had relatives in Tucson. However, a diner in Tucson was named Alice's Restaurant, after Arlo's famous movie. I wonder if he ever visited it?