> Hypothetically, should a party running on a platform of ending democracy be allowed to participate in democracy?

I think any party not encouraging others to commit violence should be allowed to run, if majority of all voters don't want democracy, it should be their right to vote for such party, which wants to end democracy. Democracy is here for the people/voters, not vice versa, it should have no self-preservation mechanisms, if it has it's not really an democracy anymore, if opinion of majority of the people is not respected to preserve it.

> Should they be allowed to end it for all future and current citizens?

Well, look at the Brexit referendum, it's kinda same thing.