If an Exception happens within a using statement does the object still get disposed?

Yes, they will.

using(SPWeb spWeb = spSite.OpenWeb())
{
  // Some Code
}

is equivalent to

{
  SPWeb spWeb = spSite.OpenWeb();
  try
  {

    // Some Code
  }
  finally
  {
    if (spWeb != null)
    {
       spWeb.Dispose();
    }
  }
}

Edit

After answering this question, I wrote a more in depth post about the IDisposable and Using construct in my blog.