Upon changing the IP on a SonicWALL, it will send out both classical gratuitous ARP broadcasts as well as other effective 'non' grat ARP broadcasts to inform upstream and downstream devices that the IP has changed to the new Ethernet (MAC) address. The Sonicwall OS has been around since the last millennium. It has a lot of code incorporated which will allow proper standards conforming devices as well as the plethora of 'one off' devices to understand changes that occur when a fundamental change such as an IP change occurs.
A bit of advice- when changing IP'ing, upon completion, it is generally a common sense and pragmatic idea to reboot the connected devices. IP changes often will occur seamlessly but a reboot never hurts.