There should be no problem getting to Sosua from Santiago without a reservation. The bus starts in Santo Domingo, usually makes a quick stop in La Vega, then goes to Santiago. If you were boarding the bus in La Vega you might have a problem. If the bus left SD full and nobody got off in La Vega, then there would be no seat. But a lot of the passengers on the bus get off at Santiago, so that when it goes on to Puerto Plata and Sosua, there are a lot of empty seats.
If it were me, I wouldn't worry about having a reservation for the trip from Santiago to Sosua. There will be people, like you, buying a ticket in Santiago for Puerto Plata or Sosua, but not as many as got off in Santiago.