Since the record of Russian AD taking out Storm Shadow is not great a strike with low observables like JASSM likely to succeed if the bridge is guarded by S-400. Though ATACMS has never been tired against the system either so while technically it should be able to defend against it the Russians often exaggerate capabilities.
Ideally a complex strike with converted S-200 missiles, JASSM, ATACMS, and MALDs would be very likely to succeed I think.
We have seen GMLRS get shot down by Russian AA, and we have seen entire salvos of GMLRS punch right through Russian AA like unstoppable golden super weapons while Russian AA fires interceptors ineffectively.
I suspect ATACMS would perform similarly. Some would get shot down, and some would punch straight through.
I do not think it is the GMLRS rocket that is the super weapon. I think it is the Russian AA QA that is the issue. Those same QA failures will allow some ATACMS missiles to copy GMLRS successes.
In other words, Ukraine does not need a stealthy super weapon when 1/2 the Russian AA systems are defective.