No, the intent of sanctuary cities is that they do not attempt to go after illegals if they have other contact with the system. The intent is to allow them access to things like law enforcement so disputes are settled legally rather than by violence as they are in the criminal world.
It goes far beyond that. It prohibits local LEOs from assisting federal immigration authorities in any way, and in fact they hinder them actively too.
That case where an illegal killed a woman (and got away with it thanks to a SF jury) is probably one of the most egregious uses of "sanctuary city" policies. Zarate, the illegal, was already in federal custody, but was transferred to SF for a local matter to be adjudicated. After that was done, he was simply released into the wild and not returned to ICE custory because SF is prohibited from assisting the feds. That's messed up.