If Szeth had bonded and suppressed a spren Shallan style(something I don't think he would be very good at) I think that either Nale or the Spren themselves would have noticed. There are a number of ways Szeth could find out about the imminent voidbringer assault. Future sight would work as would spren informants, knowledge of a budding Radiant, hearing a death rattle, or perhaps one of the Honorblades does something odd.