Third parties can bring the pressure on the two party system.
In theory yes but the .05% who vote third party are generally ignored because they don't have the numbers to pressure anyone. Despite your hammering on the subject, I am still of the belief that the Democratic party is salvageable. It has to be because there is no viable third party on the horizon. There is, however, a rash of idealistic left leaning Democratic candidates looking to push out some righties in this election...and pull the Democratic Party left when they do.
The TEA Party was a brilliant example of how third parties work in our system. And the Green Party an example of how they fail.
The TEA Party worked within the Republican Party to change it by running against moderates in the primaries. It worked and we have Trump to show for it.
The Green Party set itself up as an alternative to the Democratic Party. It hasn't worked out. Even Bernie saw the value of working with
Democrats rather than against them. He didn't get elected but his campaign in 2016 pretty much wrote the platform for progressive Democrats who will win today. And their victories will pave the way for future progressives to run and win.