Are you sure you’re talking about an actual credit card or a debit card tied to your bank account?
Your card may read Visa or MasterCard, but it can be a debit card. What you say makes no sense because credit cards are not tied to a bank account, so even closing a bank account doesn’t mean that you need to close the credit card account as well.
It makes sense if it’s a debit card, because they ARE attached to a bank account, so switching bank account requires issuing a new card.
To answer your question: The activation process is just a security measure, and has nothing to do with the account. The account is open, accrue fees and interest and will show up on your credit report whether you activate the card or not.
If you’re not planning on using this credit card, close it via a written letter and request conformation that it’s close with a zero balance. Keep it forever. It’s not unheard of for people to find a charge-off on their credit report from a credit card they thought was canceled. Please see close-credit-card.html for more information. Follow the instructions there and use the sample account closing letter.
Closed accounts in good standing will remain for at least 10 years on your credit report. They have no negative effect on your score. They just don’t count much as open, active accounts.