As far as I know, the serial number doesn't have anything to do with the network accessibility of your Mac.
The MAC address can only be used to find your IP address (in general) if someone else is on the same local network. Again in general, knowing the IP address of your Mac doesn't really give that much information as far as "hacking" it is concerned - without sharing services turned on and an account enabled for those services for which your adversary knows the password, there's not much they can do over the network.
I'd have to know more about your situation (what networks is your Mac used on?), the nature of your adversary, and the type of attacks you are concerned about to comment further.