No, you cannot counter Dragonlord Dromoka with Voidmage Apprentice.
Dromoka cannot be countered at all, it doesn't matter what is trying to counter it.
Also "When ~ is turned face up, ..." is a triggered ability. So flipping a card face up is a special action that doesn't use the stack, and once the card is face up its ability triggers and is put on the stack.
If instead you were trying to counter something like Abrupt Decay that "can't be countered by spells or abilities." you still couldn't counter it because you would still be using an ability to try and counter it. The "by spells or abilities" rider is there on spells with targets so that if a spell has no legal targets it can still be countered by the game rules.
The answer to the question as written is no. But, the answer to the question in the subject line is different.
The answer is, it depends on your definition of "counter a spell."
If your definition is the usual, technical definition, then as other answers have pointed out, you cannot counter a spell that cannot be countered.
However, if your definition is a bit broader, such as, "stop that spell from resolving, no matter what." Then the answer is YES. Here is what we've found so far:
- Remove the Spell from the Stack. Venser Shaper Savant, and Brutal Expulsion are cards that directly return spells from the stack to their owner's hand. This is a tempo play, but sometimes that's all you need.
- End the turn. Here, Time Stop, or if it's your turn, Sundial of the Infinite are two options. If you have a way to cast sorceries as instants (for instance Hypersonic Dragon) you can also use, Day Undoing but only on your turn will it destroy the stack.
- Kill the player. Sort of obvious, but if you're in a multiplayer game, and someone is casting that creature using a flash ability during Bob's turn, you can "just" kill Bob while that spell is on the stack, and that will stop the spell from coming into play.