Hi,
just keep in mind that maximum hardwired cable length is 50 feet for hardwired failover. So you have to have your cluster in the same datacenter and also have a 50 m cable :-), in any case I recommend you network failover features.
for more info:
https://support.f5.com/csp/article/K2397
So to answer to your question, YES you can use Business Interface in order to deployed HA (waiting to solve your problem). So for sync you can use your Interface Business and for Failover you can use your interface business too and you management port.
Just don't forget to change business interface (selfIP): Port Lockdown To ALLOW ALL.
as far as I'm concerned I always put a secondary interface (Business interface /mgmt interface) to take over if my HA interface has a problem (In order to avoid conflict IP, ...).
Last point you just need to know that when you sync (using business interface), synchronization consumes a lot of bandwidth and could potentially impact services. that's why F5 recommends a dedicated interface.
Let me know if you need more details.
regards