No. Clients cannot see the events on your Grow calendar or on your personal calendar. All they will ever see are the dates and times you are marked as available.
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Below is a screenshot of the public provider directory, where new clients can view availability and self-select appointment times:
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Additionally, existing clients will also see this view when rescheduling an appointment with you:

Grow Therapy's scheduling system automatically adds appointments to your synced calendar as events, which are only visible to you by default. The event name by default is [Your Name <> Client Initials].

The example below shows how events appear on a provider's synced calendar using Google Calendar:

Clients see an identical event view, and its details also include instructions on joining or managing their appointment.

Additional information on managing your appointments and schedule is available in this collection of articles.