They are still able to force a new IP onto your router.
Even if I set the router to static?
If this happened your computer would stop being able to use the internet. The ISP would reject your packets due to not owning the IP. This is the basis behind a DHCP based internet gateway.
The router will obey you but the ISP will not obey the router.
Unless you hacked the router, it wouldn't send any packets at all. It would never bring the IP link up because address negotiation had failed. Even if you did get it to accept packets, no packets bound for that address would ever get back to you.