Push notification on Samsung Galaxy Note (GT-I717)
If you would like something on your screen in addition to the notification in your notification bar, I would suggest using something like GoSMS with WidgetLocker.

If I'm correct in your understanding, this will do what you want: Set up WidgetLocker to be your unlock screen and then place a GoSMS messaging widget on your lock screen, so you can read the messages immediately. 

I don't know if this is what you are looking for, but I hope it helps!