No, but you can ask someone else to buy it for you However, you cannot activate it, since in order to activate you need your own credit card.
If you need a referral code, this is mine K61CD in order to have 25$ after your 2nd payment, import to be used during the plan creation on the last step where the total with the taxes are shown.
As Mike stated, plans need to be paid by credit card, with the name and address associated with the card account holder matching the information entered into the payment information in your Fizz account. So while may be able to convince a friend to purchase the SIM for you, it might be a harder to convince them to allow a recurring monthly charge to be applied on their card.
But if you have a REALLY good friend, it might be worth asking.