Yes.

You must be online when downloading the app, entering the applippli-key, and activating it.
Also, each customer has their own expiration date for monthly or yearly payments, so you should expect to be online at least once a month.
Even if you pay the monthly fee or renew your yearly payment on your My Page, if your PC remains offline for a long period of time, the expiration date will not be updated and you will no longer be able to use two-step authentication.