In my experience, no.

Having said that, I don't use a Samsung phone. All other messaging apps I've used on other phones had the same behaviour. If you have that specific message thread open, you will not receive a notification.

If the screen is locked, you are viewing a list of message threads or the app is not the active app, you will receive a notification. When viewing the actual message thread, you will not receive a notification.

That behaviour caught me out several times when waiting for a response, I get distracted with something else & suddenly thinking I hadn't heard back from that specific recipient, only to discover, their message is waiting there, open on my screen.

My Motorola gives a very faint 'plop' sound, so like ANglEAUT often miss the incoming message if away from phone.  Bit of a bug on phones really?