Brandon has said that Szeth is not on the path to Radiantness like Kaladin, something different is happening with Szeth, so yeah, he's probably not bonded to a spren like Kaladin is.
also, Syl made it clear at one point that she could break the bond between herself and Kaladin, so I'd imagine that if somebody bonded to an honorspren started acting really dishonorably the spren would break the bond.