Can users manage their own subscriptions?
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.
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.