Does having a load balancer allow you to re-use socket connections?

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http://serverfault.com – I have a service where servers upload 20kb xml files to my server. There is no session, it is a single POST request and that's it. Each individual request is authenticated based on the contents of the xml file. There are socket related tweaks that I will have to make as during load testing the server exhausts its sockets pool (32K). Anyhow, I was wondering what things might change when I bring a load balancer into the equation that would round robin requests between 2+ web servers. Could the load balancer re-use sockets? Again, just want to be clear, client servers are posting a file ove (HowTos)