I think "stowaway" is a bit strong of a word in this case. It's not like the OP would be hiding from the conductor...he would be making a good faith effort to purchase a ticket. I also think Acela conductors are probably reasonably aware that fares from RTE are usually (always? I'm not sure) the same as from BOS or BBY.

That said, if you're boarding the train in BOS you should have time to complete the purchase before the actual departure time, shouldn't you? (Assuming you have the App at the ready and are familiar with the process.) Once you reach your seat you should have a minute or two before the train pulls out and certainly plenty of time before the train leaves BBY which is when it would really start to "matter." Just settle in to your seat, buy a ticket from BBY-NYP and you should be good to go. If the train shows up as "sold out" just get off in BBY, head back to BOS on the next MBTA and resume Plan A.