Yes, a server side "script" is just a program, typically with specific interfaces for communicating back to the client but it can really do anything. What is it you actually want to do?
I assume what is being asked for is some process that can be initiated through a standard http-request but then doesn't need that browser to remain connected for it to keep going, and the answer is yes, absolutely. You can use CGI to get the parameters of the request, send back a response, close the connection, and then keep going.