Someone is trying to assign their own static IP on my network. Can they access the internet?

I see that on my network, someone is trying to assign an IP address to some sort of device on my network.

I have a multitude of rules set on my tomato router for QOS that use IP addresses as part of the rules so that it's critical that there are no errant IP addresses on my network.

I have an automatic assigned range which have their own rules, and I have specific IP addresses for know devices on my network.

If an unkown MAC address tries to assign an address outside of the assigned range...

Someone is trying to assign their own static IP on my network. Can they access the internet?