I understand that, but this is a very infantile way of "making a point" a sort of "to piss off my mom I will cut my finger." Given the nature of the US political system, GP would "make a point" much more effectively if it formed a nominally nonpartisan bloc willing to support any political candidate with the right policy proposals, regardless of political party affiliation.
That was the clever strategy of Tony Mazzochi of the Labor Party. The fact that LP was a flop was due not to its poor electoral strategy but the fact that the clout of organized labor is nearly zero - the unions have almost no capability to tell the rank and file how to vote (the rank and file is more receptive to socially conservative agendas than union appeals), all they can do is to contribute money.
The Greens and assorted lefties, by contrast, have a much greater persuasive power which they can strategically use in close-call elections - if they did not waste their energies on running candidates attracting less support than the margin of statistical error.
Wojtek