Chemical exfoliating cleansers sound like a simple way to perform two steps in one. Unfortunately, they don't actually perform any meaningful exfoliation.
At home chemical exfoliants work over a matter of hours, not minutes. However, when you wash your face, your skin is only in contact with the cleanser for about 15-30 seconds. Therefore, there just isn't enough time for the chemical exfoliating ingredients of a chemical exfoliating cleanser to do their job. So really, a chemical exfoliating cleanser is just... a cleanser. There is no added benefit from the exfoliating ingredients.
There is another obstacle preventing your chemical exfoliant from working. Glycolic is water soluble, which means that as soon as you apply your cleanser to your pre-moistened face, the glycolic is deactivated. Salicylic acid is however not water soluble, but it is still not in contact with the skin long enough to have any effect.
Exception to the Rule
There is one exception to this rule (isn't there always?). Cleansers that contain physical exfoliants can effectively exfoliate in the short amount of time they are applied to the skin. The exfoliation results will be directly proportional to how long you rub in the cleanser and how much pressure you apply. That doesn't mean that more is better! With physical exfoliants, the chances of irritation are greater, which is one of the reasons that chemical exfoliants are preferable.
So while combination products do make life easier, be sure that it makes sense to perform the two actions together.