No, a Yahoo! ID or Yahoo! Calendar is not necessary to respond to a Yahoo! invite. When your guests receive an invite, they will need to click the link to bring them to the invitation page.
At this time, they will be prompted to sign in to their Yahoo! account (if they already have one) or to sign up for a Yahoo! account (if they don't currently have one), but they do not need to do either in order to reply to your invite.
If your guests do not have Yahoo! IDs, we recommend they sign up for a free account before responding. After they activate their Yahoo! Calendar, they will be able to see invitations on their own calendar.