The standard says that:
When a client or server wishes to time-out it SHOULD issue a graceful close on the transport connection. Clients and servers SHOULD both constantly watch for the other side of the transport close, and respond to it as appropriate. If a client or server does not detect the other side's close promptly it could cause unnecessary resource drain on the network
In the real life you should distinguish the logic that implements HTTP standard and the logic that implements a business feature. Will the business logic still be processing after the HTTP server detected that the connection has been closed depends on how the server is implemented, how the business logic is implemented and how wverything is integrated into each other.