No. The card in your Baby's First Year Gift Box has a gift code for one 12-month, 5x7" Softcover Baby's First Year subscription. It isn't a Chatbooks Gift Card and doesn't add $150 or any dollar amount to your account. It can only be redeemed for one 12-month, 5x7" Softcover Baby's First Year subscription.
Baby's First Year gift code: starts one 12-month, 5x7" Softcover Baby's First Year subscription. Redeem it at store.chatbooks.com/gift/redeem-amazon
Chatbooks Gift Card: adds Chatbooks Credit to your account that you can use on subscriptions and books. See How do I redeem a Gift Card?
Chatbooks Gift Card sold on Amazon: the $25 Chatbooks Gift Card is sold on Amazon on its own. It's a physical card and isn't included in the Baby's First Year Gift Box. It adds Chatbooks Credit you can use on your subscriptions (Monthly Minis, Monthbooks, Baby's First Year, and Prints) and on Classic and Layflat books. It can't be used to purchase gifts, like gifted subscriptions or Gift Cards.
If you enter your code in "Redeem a Gift Card" or the promo code field, it won't work. Use the steps in How do I redeem my Baby's First Year Gift Box code?