Network failover through the management inferfaces

It can work, but why bother? I assume that you prefer to keep the number of interfaces to a minimum. It's better to not use the management-plane for TMM operational purpose. I suppose that for network failover and config-sync features alone, it's a less significant of a choice that ultimately comes down to a matter of preference. On the other hand, for the more resource-intensive HA features (traffic mirror/sub-table mirror/persistence mirror) it's a matter of right and wrong.

So I'd recommend to avoid using the mgmt interface for HA :)

Tip: Use the non-routable IPv6 link-local addresses for HA SelfIP purpose. You can re-use the same addresses for all your BigIP implementations, regardless of network design. (very easy to automate, one less variable to consider)