No. They're only useless if the company fails to execute on the demand that is created by the shortage. A company with a history of trickle-down-product will never fail in this regard.
This should be obvious, but the money is made by the interest that is created through supplying an absurdly low amount of product to stores. More interest, more buyers, more money. Nintendo is not run by people who forego forecasting, demand planning, and inventory management. Nintendo is also not a business that operates with disregard for quarterly results, so rest assured they'll magically find a way to meet demand aka make as much money as possible on the NES Classic before the quarter is up.
Others can't profit from the shortage of the NES Classic because others -- Sony and Microsoft -- don't make a NES Classic. This isn't a $60 third-party game where one version of the game ran out and isn't available. Of course, some stores do stock those 100-in-1 unofficial consoles, but due to the legalities of the product, the stores will never have the consoles in mass market quantities. The NES Classic is a unique retro product, and shortages of the product give Nintendo a lot of legroom during negotiations of shipments, replenishing stock, retailer cut, and overall stock distribution.
If you care about learning more on artificial scarcity/the scarcity principle, here's a great article that talks about it:
http://www.referralcandy.com/blog/hurry-stocks-last-13-examples-scarcity-principle-used-marketing/