"But what if most of the consumers don't redeem the CP? "
This is out-of-scope. The company does not need to drive MOST of the coupon holders to try their coupons and become loyal customers. They just need to increase the number of their customers.
Let's suppose the company issued 1000 coupons, 300 of which are redeemed by customers. And these 300 customers finally become loyal customers. Then, this plan is deemed successful, because it attracts 300 potential customers as loyal customers.
B is hurt. Customers who seek cents-off coupons are less likely to be loyal customers irrespective of the brand for which the coupons were offered. Correct.