Yes you should be able to get back on the train at will. Way back in '03 I was riding the train back home to Miami after visiting my family in New York. When we pulled into Washington I went into the station called my mom from a pay phone (this was before my then adolescent self was able to afford a cell phone) and then found a stairway back onto the platform. All this happened within 15 mins of the train pulling into D.C..
On a bit of a side note I have a question. I'm based in Norfolk and every once in a while I ride the train from Newport News to NYC to visit my family. My train ride is preceded by a Thruway bus ride from Norfolk to the station in NPN. So far I have always had my tickets in hand. My question is if I were to buy my tickets and select the pick-up from station option would I be able to get on the Thruway bus?