Failover using BGP works as well as the BGP failover works... The only issue you'll have is with keeping the LTM configs synchronised between the pair in DC1 and the pair in DC2. That'll be either manual (Copy config file and restore - which does shared config only if the hostname is different), or you could script it via ssh/bash or iControl via Java/Perl/Whatever.
(Some assumptions made here - YMMV :)
-Assumes IP ranges are same so shared config can be loaded across all 4 units etc. So if DC's have different ranges and youre' NAT'ing the inbound traffic at the DC border, and just using the BGP to get to the external facing IP, there's be a bit of config 'cleanup' to be done in order to use synchronisation across the F5's. The remedy for that is a bit of intelligence in whatever you use to sync the configs... EIther a bit of perl to massage the configs, or change it when using iControl etc.
H