Does the invading player need to remove Draco before attacking the ancient?
No, the rules are the same as if Draco didn't have an influence disc there: players have to fight each other first (Draco included) then the survivor fights the ancient (unless Draco survives obviously
Once the attacker has killed the ancient they can attack Draco's planets.
Does the Draco player immediately claim the tile?
No. If Draco's planets survive the assault he must re-influence the sector to claim the discovery tile (because you only get discovery tiles when you place an influence disc).
However, remember that you can't influence a sector where there is an enemy ship, so as long as the attacker stays in the contested sector Draco can't claim the tile.
Hope that was clear?
Proof from the official faq that is pinned to this forum:
Q: If the Ancient Ships are destroyed from a Descendants controlled hex but the Descendants still control the hex, can they take the Discovery Tile?
A: The Discovery Tiles can only be taken when placing the Influence Disc. So you'll first have to remove the disc with the Influence action and then place it again.