Great Wyrm + Spellcasting?

[Uhtred]

So, say, hypothetically, that a Great Wyrm Silver Dragon Elected to...IDK, eat all of hell to gain enough experience to gain his first character level, advancing from his 29 hit dice. He's already casting as a 19th-level sorcerer with a caster level of 19, but suppose he elected to take Sorcerer as his first actual class level. Is he now casting as a 20th-level sorcerer, or does he only gain the Bloodline Power and Eschew Materials feat that he gets as a 1st-level sorcerer, and casting doesn't advance until his character level catches up to his hit dice in terms of casting? Or does he get the 3 additional 1st-level spells from being a 1st-level sorcerer in addition to the ones he already has from casting as if he was 19th-level? It's confusing, but I AM trying to do it right.

[Psyren]

Yes - class features that are shared by a monster and any class levels you're adding to it do stack (Bestiary pg. 297.) So you would indeed get to add the sorcerer level to the dragon's innate casting.