Yes, I think that a tie should be allowed if both kids are able to spell the same word right over and over again. Just like in the National Football League which also allows ties, I think that a Spelling Bee should have two winners and that would in no way cheapen a win.
While a tie isn't the best outcome in any competition, I do not see the harm in allowing a tie in an academic competition. If both spellers prove their merit by repeatedly spelling insanely difficult words correctly, without faltering, it is a completely legitimate outcome to declare a tie and award both competitors the top prize.
If the contestants spell all of the pre-picked words correctly and there are two or more contestants left then I think there should definitely be allowed to be a tie. These kids have worked very hard and I don't think there always has to be one winner especially if they both have very similar if not exact skills. I think there is room to celebrate both.
No, I feel that ties should not be allowed in the National Spelling Bee. These kids spend months on end not only learning the words, but going to school, participating in extra-curricular activities, and finding time to be a kid. When they win, it should be a triumphant moment that they don't have to share.