No, the A10 (and most other hardware load balancers) functions as a proxy -- all the traffic flows through it:
Clients <-> A10 <-> Cluster Nodes
The clients never talk directly to the nodes.
On the A10 you configure a policy so that traffic is sticky (always goes to the same node) based on some set of rules, and you have health checks so it only sends traffic to nodes it knows are responding.
With hardware load balancers you have to be careful of single point of failure. i.e. if you have multiple cluster nodes, but a single load balancer, then you've only moved the problem slightly higher up the stack. The ideal solution is:
2 Datacentres
2 Load Balancers in a cluster (either Active/Active or Active/Hot-Standby) per Datacentre
GSLB (Global server load balancing) -- uses DNS to route the traffic to one datacentre or the other
If you are REALLY lucky, you get stretch VLANs (the same subnet in 2 datacentres), and you don't need to use GSLB, although there are still reasons to use it (it depends on the hardware implementation of the load balancer, i.e. manufacturer specific).
A10 is really really good value for money.