No. It's the application server's business to accept and handle incoming http connections - and you can help it by occupying one connection for as short time as possible. Doing so on your own would totally pollute your own code with appserver duties and you should not want to get into this kind of business.
The comments on your question give some great suggestions for alternative solutions. As long as you keep sitting on a connection (or request/response pair) it will be busy and not available for the appserver.
Alternatively, with your load profile, you might be able to just increase the number of concurrently handled requests - if they're really mostly idle and waiting, this might be a good quick fix: You can potentially handle a lot of other requests while your long-running requests are waiting for the background processing. Not that I think this is elegant, but it might be the quickest fix.