Was it possible for the apostles to travel across the known world in seven years with ancient transportation?
Yes. According to the context, even with the transportation of that day, the twelve apostles could have covered a good part of the then-known world in seven years, and should have covered the Roman Empire. They remained in Jerusalem because they could not go beyond Israel's borders until Israel had her King.
Les explains that the expectation was that within seven years the twelve should have covered the Roman Empire. Even using the transportation of that day, they could have covered a good part of the then-known world in seven years. But they were still in Jerusalem, and they were not derelict in duty. They knew they could not go beyond the borders of Israel until Israel had her King. Their whole driving momentum was the hope that Israel would repent of having crucified their Messiah, so Christ could turn and set up His Kingdom. The context then points to Zechariah 8:20, where God says it shall yet come to pass, showing that what Israel was to do regarding the Gentiles and the rest of the world was still future; they had experienced David and Solomon's glory but not what God had promised.