Hi,
Rubbing alcohol is great to loosen contaminants and clean away flux/corrosion residue if it is done correctly and using a cotton or a foam swab.
However, if you have any dirt or debris on the device, alcohol will just loosen them and carry them along potentially causing other issues if it is not cleaned properly.
The stick drift is actually caused by the worn part of a potentiometers, nothing that rubbing alcohol would sort out.
If you are in a position of disassemble the device and get it cleaned in an ultrasonic cleaner would be my first recommendation as the alcohol and the contamination probably seeped in to the intricate parts of the device.