Dragons aren't spirits, however. They are living, breathing creatures, who just happen to be bigger, stronger, more intelligent, older, and tougher than you will ever be. And unlike other Name-givers, they get stronger the older they get. Their abilities fall into two categories. They have their racial abilities (same as elves have low-light vision, and trolls have natural armor), and they have their magical abilities (spellcasting and conjuring). Just as a troll doesn't get any stronger when there's a background count, neither does a dragon's hide get thicker. A dragon's hide is thick because he's been growing it for a few thousand years.
Yes, dragons could be brought down with magic during the Earthdawn period. But it took a lot of magic, even at the height of the mana cycle. Even Great Dragons could be killed. Of course, it took an airship that was basically a chunk of mountain held aloft by magic, with a small army of magicians and people using magical cannons, but yes, Great Dragons were killed. And they could be killed in Shadowrun, too. It is difficult for metahumans to kill Dragons, even the normal kind, but it is possible. Could Sirrurg, Lofwyr, or Hestaby be killed? Of course. Could metahumans do it? Certainly. Would it take an army? Most definitely.