What Joel said is correct. In addition in SL3 you can decide to use Silverlight's networking infrastructure instead of the browser's one. You switch to it with
HttpWebRequest.RegisterPrefix("http://", WebRequestCreator.ClientHttp);
Be careful because in that case the OS proxy settings are used instead of the browser settings.
As for out-of-browser mode, I just did a simple test:
var req = HttpWebRequest.Create("http://www.google.com");
if (req.CreatorInstance == WebRequestCreator.BrowserHttp)
MessageBox.Show("Browser");
else
MessageBox.Show("Client");
and found that the browser's stack is the default in OOB too. They probably load some IE component, thus it should use the IE proxy settings as well.