Yes, most tracking units are built into the integrated circuits (mobo). Most tracking stickers are fakes and don't really have hardware tracking at all.
The IP will change according to whatever the DHCP server on the private network he uses it on. It won't help.
Even if it's used on the same network, it will lease a new address since the swiped HDD lost the last leased address unless that net uses static DHCP which circumvents the reason for using it so most don't.
If it's used on anther net, you'll never see the MAC address again because it's a physical address and not routed. New mobo=new WiFi NIC=new MAC
Just adding that in there before someone brings up MAC address.
You'd be shocked how many people on my home board argue that MACs are routed on the Internet...