It does on my machine, but I can't see that it's documented to. I'd certainly expect it to by default. The simplest way to tell is to run Wireshark (or Fiddler) and look at exactly what's going down the wire.
For example, this program:
using System;
using System.Net;
class Test
{
static void Main()
{
WebClient client = new WebClient();
for (int i = 0; i < 50; i++)
{
string text = client.DownloadString("http://www.microsoft.com");
Console.WriteLine(text.Length);
}
}
}
Generates a first request of:
GET / HTTP/1.1
Host: www.microsoft.com
Connection: Keep-Alive
Subsequence requests are just:
GET / HTTP/1.1
Host: www.microsoft.com
... presumably because once a connection is in KeepAlive mode, it's assumed it will stay that way.
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