I think you can check the status of it on the bungie site , otherwise if your friend has been around for more than 7 days (pretty sure beta play counts as well as demo) you're out of luck.
This is what it says in the status page:
[b]LINKED FRIENDS?
Your Refer-a-Friend quest progress:
PlayStation Quests
Visit the Speaker in the Tower to start the Questline "A Tale of Two Guardians".
PENDING REFERRALS?
Friend status:
Generated Code
https://www.bungie.net/en/ReferAFriend?code=XXX-XXX-XXX-XXX
Remove Referral[/b]
He still has a few more days left and he never played the beta or demo.
Your referee has not accepted your code.
If they accepted the code it would show your referrals GamerTag.
Please ensure that the link you send is clicked by your referee.