Yes, you would know 9th level spells..and I think as many as you normaly would at level 20 with the Sor 15 Arch5 Dragon Disiple 5 but dont quote me on that..
Flavour advice: Either or both of those pretige classes are great for a lot of sorcerer character concepts. With the Archmage, your...well...an Archmage, a true master of magic. With the DD your delving into the rumours of sorcerers being desended from dragons. Those two are pretty easy to combine.
If you want something with strange flavour, the Alienist is a sort of Lovecrafty prestige class.
The epic spellcaster prestige class...dont remember its name..focuses on summoning creatures, dimensional travel, and planar oneness. Its in the epic handbook