Although I am not a parent and have never traveled on Amtrak with an infant, I really would not worry about getting a ticket for a person who's not going to be occupying his/her own seat. I don't think the conductor will care one bit. I would just get on the train--don't mess around with the ticket window at NYP, which is a nightmare--and if there is any issue with the conductor, plead ignorance. But I don't think it will come to that.

If someone has experience that contradicts my assumption, I'd be interested to hear it!