Dragons certainly can talk; Reefclaws is an exception stated to clarify.
The Dragon monster type has linguistics, bluff, diplomacy and intimidation listed as class skills, and certainly one or two of these could be justified as being used on their own without speaking but not all of them.
Dragons themselves are listed in the bestiary with multiple languages and, crucially at later ages the ability to cast spells as a sorcerer:
Spells: A dragon knows and casts arcane spells as a sorcerer of the level indicated in its specific description. Its caster level depends on its age, as shown for each type.
Casting spells as a sorcerer for the most part will require a verbal component, without this the dragon is going to be very restricted in it's spell selection (without using feats).
So at highest restrictiveness for dragons you could rule that before the dragon can cast spells it can't speak, but I think this is splitting hairs.
Note that in the creature types humanoids are listed as being able to speak, as are several other types; however known (presumed?) speaking creature types such as Brownies, Dryads and pixies are listed as type fae (Not Humanoid/fae) which isn't listed with the ability to speak. Certainly the Brownie at least as listed in it's flavour text as speaking, whilst the Dryad and Pixie are not.
When it comes down to it, as usual, what the GM wants. Speaking dragons are, after all, an exceedingly common fantasy trope.