Is "The Best Meat Buns" a double entendre in Japanese?
You might be overthinking this. 

Remember that this is at a cultural festival. Natsu with the ad on her back, wearing a China dress, is more likely out there to be a poster girl of sorts to advertise her class's themed cafe,inside the building. 

If a double entendre was intended it would make more sense to put the ad on the front versus the back, below the actual goods. Even if this were true, why advertise the class when the advertised product is right there?