Hi Terje,
Thanks for reaching out to us!
This is only “partially” possible if you require people to log in before being able to make RSVPs. So those RSVP responses become linked to the user account.
There is a great article on how you can Display a List of Attendee’s Events so the users can log back into your site any time and adjust their RSVP or registration information. Yet, there is no built-in functionality to provide the users with an export of all those upcoming events for them.
It is an interesting functionality though, so I encourage you to go into UserVoice and post that as a feature idea so other users can vote for them.
I hope this helped!
Best!
Victor