No, why would it? It will run code in the context of the current user which is absolutely enough to start a new process that will run in the background, download more code from a attacker server and allow remote access. The attacker will only have as much permissions as the user executing the code but that is enough to steal their files, run a keyloggers, steal their sessions for other websites etc.
They can try to escalate to the admin user, but when targeting private victims, all the data that is worth stealing is available to the user and does not require admin privs.
The post office knows who you are sending letters to. They have to know because they have to deliver it. They do not know the content of the letter. They also dont know if the letter will be passed along by the receiver to a different destination.
Your ISP knows you are sending traffic to a VPN but not where they are sending it to. The VPN knows where you are sending traffic to but not the content of that traffic. So if you browse a website that only serves pirated content, then they knows you are consuming pirated media but not which media.
If the law requires the VPN to report any and all traffic to blacklisted sights then a “no logs policy” would breach that law.
However to make this law work, Italy would have to ban all VPNs and http proxy services outside of Italy. Italy would have to force pretty mutch the whole world to follow this law for it to work.
What happens if you run a tiny server on AWS in the USA to proxy your private traffic. Unless AWS USA is watching all traffic to see if it complies with Italian law there is no way to enforce it.