Q: in that case will the client to load-balancer connection be http2 ?
A: Yes, it will be HTTP/2
Q: if client side establish connection on http2, then would that give any performance benefits by only running http2 on client side?
A: The F5 supports HTTP/2 on both client and server side in v14.1.0 and later. There would certainly be performance gains to be had by just implementing clientside but perhaps not as pronounced as doing HTTP/2 full-proxy. If you were to say combine HTTP/2 on the client side with OneConnect then the clientside would benefit from the performance increase and the server-side would have a bit of a performance loss for the initial TCP handshake but proceed faster for future connections due to reuse.
Configuring HTTP/2 Full-proxy Support on the BIG-IP System