You can, but you will most likely want to bypass the Automation HAT Python library and use RPi.GPIO’s PWM functionality directly.
You will also need a 10v power supply- or possibly less if you’re not worried about achieving the maximum speed.
Is this control voltage also the fan’s power supply, or is it a separate control line? I’m guessing the former.
You would have tie the ground of your Xv power supply into the ground on Automation HAT, then connect your fan to the positive terminal of the power supply, and the fans negative terminal to the sinking output driver on Automation HAT.
I did exactly this with a PC fan on Friday.
Assuming you have a 10v supply, you should then be able to do this in Python:
import RPi.GPIO as GPIO
OUTPUT_1 = 5
pwm = GPIO.PWM(OUTPUT_1, 25000) # Second value is PWM frequency in Hz, pick an appropriate value
pwm.start(50) # This is duty cycle in %, in this case it should supply ~5v
You can then use
pwm.ChangeDutyCycle(n) to dial in values accordingly or each speed.