Well, it will be fine, but flat.
What I'd recommend doing at this point is buying some "carb tabs". You just open the bottles, drop in the caplets, and then recap (with new caps). It'll be a pain, but it will save the beer.
I wouldn't add a teaspoon of sugar to each beer, because of "nucleation points". Each little grain of sugar will cause a mini-volcano, so the whole bottle will come spewing out.