The whole thing happened within the Roman Empire, which made it possible to dispense with border hassles for a crucial period of history. This wouldn’t be like going from Guatemala to the USA; it would be like going from Georgia to Texas.
Does it mention the route taken? I’ll have to check. If the went by boat, then yes. If they went south on foot through the Sinai they would have been outside Rome. That area was controlled by thr Nabateans.