Absolutely. Each event you create has 4 options for event registration (or "who can come?"):

1. People I invite only - Once you've created the event you have the option to send personal invitations to others.
2. People I invite can bring friends - When people you've invited sign-up they can specify how many friends they will bring along.
3. Any Teamtastic member - Use this option for open events. You can send personal invitations, and anyone who finds your event on Teamtastic can sign-up too.
4. Invites and sign-ups not needed - Use this option if you don't need to keep track of numbers.

Invitations are sent by email, with a personal sign-up link.

If you have specified a max event capacity, people can't sign-up once the event capacity is reached. And it's all done automatically. No more spreadsheets!