Hello Harry
Your situation may work with simple parameters, the most of cases the requests are sent to a Load Balancer, so the requests are sent directly there and from LoadRunner prespective this is a clear process, the Load Balancer takes care of the redirections and all that, if you dont have a LoadBalancer and instead you have multiple servers or you simply need to recycle the same script for multiple servers then you may simply use the parameters if all of them are the same in terms of application version, configuration for security and few other parameters, so you simply paramterize the URL or IP´s, I would expect to also need to create some correlations in the worst case. If the servers are too diferent on the AUT configuration then it wimply will not work.
the easist way to find out this, is to create 2 scripts of the same process from different servers and compare them, there should be some little diferences specially in the URLs, but in terms of calls, ammount of calls, parameters sent etc, they should be mostly the same, if that is the case then youmay be able to make this work.
hope this helps
regards