YEs it will recover like nothing happened. You might not know this but many groomers for flowerhorn will split them like that across the whole tail so the tail can heal and become more fan like. Trust me I've seen it done and seen results. It won't harm the fish. Joey from KING OF DIY did this as well. What you can do is what until it starts to heal and cut most of it off.
Clean water and a little bit of salt will make it heal fast.
^^^Yes, I did the cutting method a lot in around tail beta, or trimming the over weight long tail beta to help them out and make the tail more appeal looking.