Yes! If you've fundraised for a previous instance of the same event, you will be given an option at sign-up (in the detailed registration process) to import your contacts (and fundraising page welcome message!) to the new event instance.
Furthermore, even if you do not import your contacts upon sign-up, or you sign up through the quick registration process, you can access that option in your contact book:
- In your fundraising HQ, click "Contact Book" in the left sidebar
- Click "Import Contacts"
- Underneath the listed services, there is a dropdown option that allows you to import your contacts from any campaign within that organization for which you have previously fundraised.