How to use HTTP Connection Manager in Script Component? (Not Script Task)
i know it's been a while since the question but i found a possible solution.

This link provides an explanation and examples of how to use the connections available in the connection manager enabled for the Script Component in the SSIS https://msdn.microsoft.com/en-us/library/ms136060.aspx

The portion of code that we are interested is this: 

IDTSConnectionManager100 connMgr;
HttpClientConnection100 hcc;

IDTSComponentMetaData100 compMetadata = this.ComponentMetaData; //Just for output purposes.       

connMgr = this.Connections.MyWebServer;

hcc = (HttpClientConnection100)cm.AcquireConnection(null);
compMetadata.FireInformation(1, "Message: ", "URL: " + hcc.ServerURL + " User: " + hcc.ServerUserName + " Pwd: " + hcc.GetServerPassword(), "", 0, ref fail);