Does LTM distribute HTTP requests or TCP connections?

Here's the question I cannot find definitive answer to: does F5 LTM distribute incoming TCP connections - or HTTP requests arriving via these connections, making load balancing decision for each request independently, regardless to the connection it arrives through and to whether it was the first request to arrive via this connection or not?

Let me explain the rationale: some CDN systems, like Incapsula, multiplex requests from multiple clients over the same TCP connection towards a backend (in our case, load balancer). This can be problematic for the load balancer. For instance, when we used FortiGate, this caused session persistence to break - because FortiGate distributes connections, not requests, even though it checks the session stickiness cookie in the first request. So all requests multiplexed into such connection ended hitting the same webserver, regardless of their own session stickiness cookie value.

How does LTM handle such connections? If cookies are used for session persistence - will it inspect such cookie only for the first request arriving via new connection (and then forward all the following requests to the same node selected for the first one)? Or will it decide for each HTTP request, which node to deliver it to, based on the session cookie of this specific request, or on absence of such cookie?

Is its default behavior customizable?