No, there is no automatism. The blocking probability by using cosmetic products with salicylate depends on

• the actual salicylate content of the product
• the frequency of use
• the used quantity of the product
• the size of the skin surface the product comes into contact with
• the time the product remains on the skin (e.g. short hand washing with immediate rinsing or applying lotion)
• the individual sensitivity to blocking effects

For this reason, Dr. St. Amand also recommends to avoid any cosmetic product that contains salicylates, since the probability of blocking cannot be estimated accurately. You are on the safe side, if you avoid consistently every salicylate source that gets in contact with skin. This will avoid blocking at best.