No.

The try...catch won't close it per se - the Using will close it...

David C formulated the question :

The "Using" should close the connection (that's the function of Using)

Hans Kesting

Let test sample code :

using (MyClass m = new MyClass())
{
    throw new ApplicationException("something wrong");
}

class MyClass : IDisposable
{

    #region IDisposable Members
        void IDisposable.Dispose()
        {
            Console.WriteLine("hey, i'm destroyed");
        }
        #endregion
}

Running using block and what you see :-)
And SqlConnection class already implemented IDisposable