This is a terrific idea, and I am glad I came across this writing of using paper wallets in this manner. It is actually extremely similar to an idea I have had in my head for about 6-8 months now and never did get written down or discussed even; so congrats on such a great concept!
I had been thinking about how to introduce a new coin project to the industry, such as at a conference or seminar, a live meet up and not an online event where along with some promotional material on basic facts about a coin and project participants would also receive a pre-loaded paper wallet. So this would go hand in hand with a flyer about the coin stats, all of the contact information namely the website and/or forum for the project and perhaps the links to the ANN Bitcointalk.org page and Twitter page.
As mentioned in this article, which I had not gotten far enough on my idea to plan other outlets of distribution, this can be transmitted electronically as well in a common email. The main difference is I was attempting to create a take away sheet with wallet that would be incentive enough for the user to check into the information about the project and if nothing more to find out about any coins received as a freebie in the paper wallet hand outs.
Random Amount of Free Coins vs Wasted Coins
The last part I tried to figure was how to, or whether to, indicate the amount of coins that are in each wallet but the amounts would range between the values received by a faucet to a higher value in a few "surprise" wallet pieces. As the idea is to acquire new members, and or at least drive traffic to the website, I thought it best to not have the amount or value readily available without first signing into a website, that can be a page of the standard site or a separate website like a faucet page. I also thought about scratcher codes, where the user can scrape off a layer and reveal the amount, like a type of lottery ticket but that likely would get expensive to print for a start-up, unknown coin.
The idea of having to go claim the coins first, whether by entering information into a designated website or by downloading a a full wallet and then attempting to collect them would be to avoid printing paper wallets with monetary values already fixed to the addresses from being wasted; to prevent printing money that is thrown away. The other concern would be how to limit or control the amount of funds, or the amount of paper wallets that can be redeemed by a single individual (as if passed out at a conference - to prevent hoarding of the paper wallets).
Claiming the Coins
So the public address could be used, without any additional "secret code", to first enter into a form to ensure that the address had not already been claimed. Some simple calculation would occur on the blockchain such as the address entered equals zero, or has no transaction record, and that would receive a "valid" reply. If the address had a balance that was not equal to zero the returned response would be "invalid". There would not actually be any coins on the paper wallet addresses at this point. Therefore no money wasted as the paper wallets would not be pre-loaded, but rather the addresses would associated to a specific, or random, "prize amount"; which means it might very well lookup another database of just the handout paper wallets and not necessarily the blockchain.
A second user entry, upon receiving a "valid" response, would claim the coins; that can be the private key. I had not gotten much further than this conceptually and certainly not to the point of how this page would make the determinations or prevent single users from claiming multiple wallet addresses for the free money. At any rate you can see the similarities of this idea using a paper wallet, perhaps users would need to register with email address & password, or the site would record the IP address; even though both methods can be easily abused.
From the original poster's idea, I like the fact of not having to know how to use cryptocurrency but earn rewards anyway but I'd think we need a more sophisticated wallet to handle many of the related transactions, although the paper wallet emailed to customer can be a great start at introducing cryptocurrency and seeing how you can actually redeem for physical goods.