Certainly you could! When your giveaway is completed and you choose a winner, if the winner selected happened to sign into the Rafflecopter widget through Facebook connect, we'll link you to their public Facebook profile along with the primary email address that's associated with their Facebook account.
You're welcome to contact winners on Facebook by messaging them. This used to be against Facebook's promotion policy, but it's been since allowed (read more on Facebook promotion guidelines here). But understand that some Facebook users have more strict messaging filters than others and might not see your message.
Your best bet to get in touch w/ your winner is to email them at the email address associated with their entry.
Lastly, if you'd like to view a more in depth view of choosing winners, check out our video tutorials.
Related Article: How do I choose and contact winners for my giveaway?