Yes, you can!
Although Yahoo's policies prevent services like ReferralCandy from sending out emails on your behalf, you've got nothing to worry about.
Just sign up for ReferralCandy using your Yahoo email (e.g. email@example.com).
Once you've set up your referral program, we'll ask you for a non-Yahoo email (e.g. firstname.lastname@example.org), which we'll use to send out emails for your referral program. And then you're good to go!
You can always change your sender email on the Email Settings page (under the Email Notifications tab).