Yes, this is standard for Stilton. It also works for similar cheeses that are lactic coagulated or use a high flocculation, and therefore have higher moisture content. You could not use fresh curds with a harder cheese like a cheddar because you couldn't spread the curds and get them to stick. For hard cheeses, you can use a spatula heated in hot water.
The reason for spreading fresh curds or for smoothing is for presentation, but more importantly for the rind. If there are a lot of cracks in the rind, the molds can get inside the cheese. And instead of forming a crust and then dying off, as happens with stilton, they would go inside and ruin the cheese. With a smoothed surface, the rind forms uniformly on the surface, mold grows, and then dies off.