No. CalendarHero helps manage your calendar the way a real assistant would, and your invitees do NOT need to have CalendarHero to accept meeting invites or see your availability.
Depending on how you invite your invitees, your invitees will receive an email that asks them to select time slots. You can also choose to send a private link or initiate the scheduling via a personal scheduling link. Once the meeting is scheduled all invitees will receive invitations and calendar updates.
To see what your invitees see when you schedule a meeting, see here What do invitees see when I invite them to a meeting?