If the DHCP server is running on local router or is at remote location where the SRST router is i.e. not affected by WAN failure, we will not run into this cold-start problem where phone will loose its IP address after DHCP lease expiry. You have to tune DHCP lease timers in such a way that phone doesn't loose its IP address. In that case phone will register with its current config and phone load.
I don't think phone will maintain its IP address info after lease expiry and phone will loose it function in that case.