Yes. Alaska allows redeeming miles with their partner airlines and Emirates is one of their partners. However, it is not necessary to have Alaska credit card to redeem miles with Emirates, you can simply be a member of Mileage Plan frequent flyer program. As a member, you will earn miles on Alaska Airline purchases and on partner airlines purchases. The registration in the program is free, so if you fly a lot with Alaska, you may prefer being a program member and not a cardholder. But if you prefer having their credit card, you can go to the Bank of America website to see if you can apply for the card (Bank of America issues the Alaska Airlines credit card).
However, please note, if a Mileage Plan account is inactive, Alaska Airlines may close your account and delete any mileage balance. You can compare the Alaska credit card with travel rewards credit cards to see if there is a better option for you. The good card for earning travel rewards is Discover it® Miles. Miles earned with this card won’t expire on your active account.