Sticky steering doesn't send your steering wheel off course as such, it feels as though someone is gripping your steering column with mole grips as soon as you stop moving the steering wheel. It is most noticeable on hot days, particularly if the car has been sitting in direct sun for a period of time and then you come to drive it. Minor steering corrections are difficult because you have to fight to overcome the stiction. The second you break free of the stiction, you're now applying too much torque to the column and suddenly you're also applying more lock than you wanted. Rather than finely adjusting the car's course inch by inch you'll be veering left and right by half a foot or more at a time. Not pleasant.
If your car is wandering around but the steering wheel is always nice and free to turn, it's more likely that you have run flat tyres fitted and/or you have worn suspension bushes and/or your wheel alignment needs attention.