It probably wouldn’t make any difference in the appearance of the belly button, because eventually it work dry up and fall off, just like if you were to clamp and cut it. There are definite benefits to delaying the clamping of the cord. There is a lot of blood in the cord and placenta that is lost that could be auto transfused to the baby if the cord is left intact.
The main problem with leaving the cord and placenta intact is that there is a risk for infection or blood loss. Also it would look really gross in the baby pictures.