Absolutely there is a connection between your line and ours. In my opinion.
I descend from Sarah Akers, wife of William Mulford (Molford) of Devon, England and East Hampton, New York, USA. Sarah was the daughter of Thomas and Priscilla Akers (from Devon, England according to our family tradition).
Your Thomas Akers, son of Thomas Akers, also from Devon, England, helps confirm this tradition, showing there was indeed an Akers family living in Devon at about the same time, and with an hereditary name of Thomas.