Accepting your calculation at face value implies that if you convince 800 (times some constant independent of n) nonvoters to vote with you, you will... (expect to) always win the election?

Your probability of swinging the election comes from modelling each voter as a fair coin flip, I believe, but this is not really a good model - if each voter is a 51% weighted coin flip then the calculus changes significantly.

Accepting your calculation at face value implies that if you convince 800 (times some constant independent of n) nonvoters to vote with you, you will... (expect to) always win the election?

Your probability of swinging the election comes from modelling each voter as a fair coin flip, I believe, but this is not really a good model - if each voter is a 51% weighted coin flip then the calculus changes significantly.