I think you won't lose anything if you try your contest idea. If you see that the result is not as good as you've expected, you can always opt for another way to attract more visitors. Personally, I am not really attracted by the idea about the referrals (when it comes to forum websites), because most website owners put some not easily achievable requirements. For example, they may want you to have a minimum of X referrals, and let's say about 50% of them should regularly post on the forum. It seems like a difficult task because you can't make people regularly post on the forum if they don't want to.
From my point of view, you may try another option - to give some bonus (let's say this gift card that you mentioned) to the top 3 contributors to the website. Thus, you will naturally fill your forum with useful information and you'll be able to generate more content and rank better. If you have another type of website (if you sell products or services, let's say), and you want to generate more referrals, then I think it would be better to establish something like an affiliate program. But, I think in most affiliate programs users receive money directly into their accounts when referring new users.
