Was the goat's blood taken behind the veil like the bullock's blood?

Les explains that after the lot fell, the high priest took the goat designated by lot to be put to death. He then took the blood of the goat, went through the same process as with the bullock, came behind the veil again, and sprinkled it upon the beautiful, golden mercy seat of the cherub. Les notes that people wonder if the mercy seat was filthy with dried blood, but the priest did not sprinkle gobs of blood; he dipped his finger in the basin and touched it, thereby presenting the blood. The scapegoat, by contrast, was presented alive before the Lord and let go into the wilderness.