No it does not. The led flash occurs when the message is sent. It doesn’t persist. The entire point the notification led on Samsung phones is to tell you repetitively that you have an unread message.

That means if you look at your phone an hour after you received the message you’ll know you have an unread message without having to interact with the phone. It’s a nice feature for someone that doesn’t like constantly checking their phone.

Besides the flash led is super obnoxious. I can’t imagine why you’d want this flashing every time you get a message. I can’t imagine it being great for battery life either.