Can I trace the caught Exception without breaking into the debugger?

Yes, there are framework classes that will give you the Call Stack information at a particular point.

[C#]
		public static void TraceExceptionCatched(Exception e)
		{
			StackTrace st = new StackTrace(1, true);
			StackFrame sf = st.GetFrame(StackTrace.METHODS_TO_SKIP);
			if (sf != null)
			{
				MethodBase mb = sf.GetMethod();
				Trace.WriteLine(e.ToString());
				StringBuilder sb = new StringBuilder();
				sb.Append('catched in File ');
				sb.Append(sf.GetFileName());
				sb.Append(', line ');
				sb.Append(sf.GetFileLineNumber());
				Trace.WriteLine(sb.ToString());
				sb = new StringBuilder();
				sb.Append('in method ');
				sb.Append(mb.ReflectedType.Name);
				sb.Append('.');
				sb.Append(mb.Name);
				sb.Append('(');
				bool first = true;
				foreach (ParameterInfo pi in mb.GetParameters())
				{
					if (!first)
						sb.Append(', ');
					first = false;
					sb.Append(pi.ParameterType.Name);
					sb.Append(' ');
					sb.Append(pi.Name);
				}   
				sb.Append(');');
				Trace.WriteLine(sb.ToString());
			}
		}

You could then call this method from the Catch portion of a try/catch block.