Can casting granted by racial HD be progressed with corresponding class levels?

Question

When a race grants a character casting 'as a third lvl sorcerer' (For example), and that caracter later takes a lvl in sorcerer- Can it now cast spells as a fourth level sorcerer? Or does it casting ability not change until it takes its fourth actual sorcerer level?

Answer 1

Yes, if the monster can cast spells "as a [x]th level [y]", then taking levels in that class will increase the monster's caster level. See the SRD on improving monsters:

A spellcasting class is an associated class for a creature that already has the ability to cast spells as a character of the class in question, since the monster’s levels in the spellcasting class stack with its innate spellcasting ability.