question on powering continuous rotation servos

Hey, new guy here to microcontrollers.

I'm trying to control two continuous rotation servos with my arduino uno and a 9V power supply. However, I don't think the arduino can supply the current that the servo will draw. Is it possible to run the power and ground of the servo to the battery and the digital line to a gpio pin on the arduino?

Thanks

Is it possible to run the power and ground of the servo to the battery and the digital line to a gpio pin on the arduino?

Yes and connect battery (and servo) ground to arduino ground for signal return path.

oh one more question. Will the servo draw whatever current it requires at the time, or does it depend on how I have it powered?

a servo will draw the current that they want if the source is capable of supplying the current. For instance a tiny coin cell can be 3V but it can never supply the amount of current as 2 (1.5V) AA batteries in series (3V). So, both.