I've been through the attempt to create an ICAP load balancer with the F5 LTM with a mobile network customer that has LTMs in their network.
Our need was to distribute the ICAP REQMOD requests across 2 ICAP server pools based on the "Host:" field contained in the HTTP message encapculated in the ICAP request body (as there's 2 distinct ICAP services running).
It didn't work! Fundamentally, LTM expects the incoming messages to be HTTP, not ICAP. We also tried to work at L3, but there's no guarantee every ICAP message will be contained in a single packet. We had to fall back to having the F5 distribute TCP connection requests.