If a spell or ability causes you to put cards into your hand without specifically using the word "draw," Messenger Hawk's ability doesn't count them
(2023-06-16) Amass Zombies works the same way, except you create a 0/0 black Zombie Army creature token if you don't control an Army
With a cost of one, she can be played in the first turn
While WotC may have seen the set as an early failure in design and production strategy, we should think of it as a microcosm of what early Magic was: a weird fantasy world where mechanics were built around the flavor and the power level between sets swung wildly back and forth, where every new set was full of new concepts as the design team fleshed out how the game would look for years to come
Her two abilities are Trance which lets you send the top two cards from your deck to the graveyard (called milling) and in return, Terra gains Flying, making her much more difficult to block
She does grow off the chitterspitter as well - so maybe you have enough incidental tokens to make her a powerhouse