Yes, you can fly with a game pad. However, I would recommend a game pad that allows you to program the individual buttons on it. AH will have no problems seeing the axis of the thumb sticks.
ack-ack
When I first started playing, I used to play with a PS2 equivalent game pad.. It worked GREAT for GV's, gunning, as well as Bombing due to everything being centrally located on the game pad, but the thumb sticks lacked the accuracy and finesse of a joystick for any remotely serious ACM.. Flying without the stall limiter was certain death..
All the buttons on my game pad were velocity sensitive.. For instance, I would press down lightly to fire the primary guns and press down firmly to fire all guns..
One the buttons I'd use for throttle, pressing down firmly on the top or bottom button(forget the letters associated with them) would effectively put me at full throttle or chop it to idle..
If I applied lighter pressure, I could actually adjust it up or down. Hit another button(sort of like shift) would turn the same buttons into RPM..
Ah! I found it after doing a quick search of my desk.. Here's what I used to use.. You could spend about the same amount of money and get a half-way decent stick..