I don't think it would/should drain/generate extra quanta.
The reason for this is that it effectively "destroys" the target creature, reaches forward in time, grabs that creature from 3 turns in the future, and puts it in the present. So it wouldn't generate extra quanta, because the Firefly 3 turns in the future is the same as the Firefly of the present. On the other hand, a creature affected by Overdrive would have +9|-3 3 turns in the future, so it would gain that buff/nerf.
Another way to think of this is that a frozen Firefly will not generate quanta, whereas an accelerated or poisoned creature will still undergo changes while frozen. In the same way, a Firefly targeted with expedite will not generate quanta, whereas targeting an accelerated/poisoned creature will make them undergo the changes they normally would.
Just my two cents.
Also, another use would be to target a newly summoned Scarab to immediately set its HP to the number of Scarabs on the board, rather than waiting a turn.