Excuse all the mayhaps, I rarely deal with database questions.
It is my understanding that a BIGIP is unsuited for SQL transactions. You would need to be able to see if it was a request for data (send it to any sql server) or adding/updating data to the table (then the data would need to go to the master sql server). You don't have any protocol visibility. Typically adding a F5 will only obscure the traffic flow.
Possible benefits: removal of common attacks on IP/TCP. SYN flooding, ping of death and similar.
The consequence (aside for the obscurity) is lack of transaction integrity (pretty sure that is the name for it). To my knowledge this is only a serious concern if you do HA active-active. Should you instead use HA active-passive you could probably get away with it.
active-passive: If you are looking for HA, but don't mind that all the requests go to the same server, then you can use priority groups. Then when the primairy server fails the traffic will be send to the spare.