Table salt has more chlorine by mass than sucralose. Moreover, in your body, table salt dissociates into a chlorine ion, whereas in sucralose it's covalently bonded into the molecular structure. That's not to say that it is suddenly nonreactive, but being covalently bonded tempers some of it's electron craving, so to speak. By your logic, table salt should be orders of magnitude more dangerous than sucralose (it's not).

Edit to add: Do you know of any mechanism by which sucralose could cross the nuclear membrane? If not, sucralose isn't going to be touching DNA at all. It could touch some form of RNA in the cytoplasm, which isn't necessarily innocent, but it's not going to be touching the DNA. That means it won't cause long-term genetic changes or damage; any damage it caused would be transitory to the working set of RNA and that damage would be gone when that RNA was processed/destroyed.