No, this law would not be upheld. We know because this actually happened: Arizona passed a state law making it a state crime to be in violation of federal alien registration laws (which automatically includes illegal immigrants) and giving state and local law enforcement the power to arrest people if they had probable cause to believe the person had committed some crime making them removable from the US. The United States filed suit against Arizona, and the Supreme Court struck down those provisions (as well as one making it a crime for an illegal immigrant to seek employment in the state, which had no federal counterpart) in United States v. Arizona as being preempted by federal authority.
Federal preemption doesn't just apply if a federal law explicitly preempts state law, nor even just if there's a direct conflict between the two. There are two more cases where it applies:
- Indirect conflict: The state law stands as an obstacle to achieving the full purpose of the federal law. For instance, in Crosby v. National Foreign Trade Council, Massachusetts passed a law banning state agencies from contracting with companies that did business with Myanmar. Then, Congress passed a law with its own sanctions, and giving the President the authority to add further sanctions. Even though the laws didn't directly conflict, the state law was found to undermine federal objectives on the matter because it banned stuff Congress hadn't and wasn't controlled by the President.
- "Occupying the field:" This means the federal government has passed regulation which is so comprehensive that it leaves no role for the states. In this case, even a state law that is entirely in line with federal law, and doesn't seem to interfere with its objectives one bit, is still preempted because Congress has implicitly made it clear that the federal law is the only law on the matter; any state law automatically undermines that.
The Supreme Court held that Congress had occupied the field on immigration: Congressional regulation was sufficiently comprehensive that there was no room for states to pass any laws controlling immigrants. So, states cannot criminalize illegal immigration because the federal laws on the matter don't leave any role for them. Furthermore, states can't give their police the authority to arrest immigrants without warrant for being removable, because that's giving them more power than federal immigration officers (who normally need a warrant), and undermines the fact that Congress normally requires a warrant before making those arrests (increasing federal discretion).