probably not.
It heavily depends on many factors, but chances are the PCB layout design and dimensions are not the same therefore not compatible.
Just look up replacement coolers for the version of the RX 580 that you have.
Or if you still have warranty on the card, use it.
You can check on warranty by googling warranty check for the brand you have (such as XFX, ASUS, Gigabyte, etc) and then entering the product number located on a sticker on the back of the card.
If you have a backplate, it would most likely be underneath it directly on the PCB.