Hi Mike,
The only issues I can think of are possible power supply and if you had set a static ip on the DNS-320. The power supply I am sure there is a work around if there are any compatibility issues and if the 320 has a static IP that is set in your NAS, but a simple hard reset, i.e., use a toothpick or whatever to insert in the reset hole on the back of your NAS. Just hold it in for 10 seconds or so with the power on. In a couple minutes, the NAS will have completely rebooted and you can log in with the default admin account and re-enter all your passwords and user accounts. This should have no effect on the data, but you should always have a second seperate backup.
You can do the reset now before moving, you should then be able to login with the defaults and just make sure you have the 320 set to get it's ip from DHCP. Should be no biggie. Good luck
PS. Ivan beat me to the punch, but the reset info is still good.