Would a 9V alkaline power a 12V DC motor?
Not for long! (And the speed would decrease as the battery wears out and the voltage falls)

9V batteries are pretty "weak" because the other half of the story is how much current they can supply at that voltage (Power = Voltage * Current). If you want to spin a big motor, the battery voltage will sag because of the battery's internal resistance. The lower the supply voltage, the slower your motor will spin. Ultimately the battery and motor will reach an equilibrium speed for the load you have on it. Check out this page to see how the 9V batteries hold up under load (hint not well).

For reference, Adafruit's 130 size hobby motors consume only 70mA with no load (battery will last ~5 hours but won't be very useful) and up to 500mA when stalled (worst case scenario and if the motor doesn't burn up, the battery will last ~20 minutes).

As you can see, the alkaline battery chemistry is not designed for rapid discharge. A NiMH, PbA or LiPo battery would be a better bet if you need more power (and you could recharge the battery for more fun in the future!)