Yes, subscribers can add their own subscriptions and can subscribe to any comment without actually commenting. First, please make sure you have enabled the "Comment Form Subscriber Options Template". Please see: WordPress Dashboard Comment Mail Config Options Comment Form Enable Comment Form Subscr. Options Template?

On the front-end, when clicking "Reply", the link to "Subscribe without Commenting" will be available. This will allow the visitor to access the Add New Subscription page where they can create a new comment subscription.

leavereply

From the Add New Subscription page, they can then add and customize their subscriptions from a number of different options such as: the specific Post they wish to subscribe to, specific Comments/ Comment Threads / Replies or even All Comments/Replies, and even how often they receive notifications for updates.

Adding New Subscriptions

add new

choose comment

delivery method