Using LMS-IP based Redundancy, the client will not request a new ip address when clients fail over, so unless you are using the same range and the client maintains the same ip address, it will not work unless both controllers are at the same site and clients are on the same layer 2 vlan.
Using High Availability Fast failover, the AP DOES deauthenticate the client upon failover, so you can have a different subnet at the failover controller: http://www.arubanetworks.com/techdocs/ArubaOS_6_5_4_X_Web_Help/Web_Help_Index.htm#ArubaFrameStyles/VRRP/HighAvFastFailover.htm%3FTocPath%3DArubaOS%2520User%2520Guide%2520Topics%7CVirtual%2520Router%2520Redundancy%2520Protocol%2520(VRRP)%7C_____5
Like you mentioned, the clients will have to disconnect and reauthenticate, but 802.1x is a very quick authentication mechanism, unless you have many many clients where your bottleneck would be how quickly your radius server can authenticate so many users. Your applications will have to recover using a new ip address, yes.
As an aside: - the majority of customers implement redundancy at the same site site with two controllers, because it is more likely that a controller would fail, rather than the infrastructure. Optionally if they chose to add another controller offsite to provide more redundancy, it is understood that something more catastrophic has occurred and that it would take time to fail over other pieces of infrastructure and getting a different ip address is acceptable. In my experience, failing over to a different site is less likely. Again, that is from personal experience. Your current design goal may be different.