it sounds like it should be possible to drive this kind of workload using LoadRunner. Either using Web (HTTP/HTML) protocol to triger the connections creation from the web, or by mimicking the web page logic using Winsockets protocol.
I would start using Web(HTTP/HTML) protocol checking what type of information in the web page needs to be parameterized or correlated in order to make sure
1. the application logic works as expected under multiple connections
2. and the amount of backend connections is as expected.
I recommend using SiteScope for monitoring the number of TCP connections on the server as well as other vital system resources to check the performance and scalability of the application.