Constantinople, and thus, the Roman Empire, fell in 1453.
There is a 16th Century Spanish explorer named Juan de Fuca who is credited with exploring the strait that borders Vancouver Island, Canada, and Washington, USA (now called Juan de Fuca Strait).
Juan de Fuca is a Hispanicization of the Greek name Ioannis Phokas. His grandfather fled Constantinople and his family eventually ended up Spain.
This means an actual descendent of the Roman Empire was exploring North America.