Yes, Conscious Politics could work within the current political structure.
But for Politics to be fully Conscious, it would require everyone operating or functioning with the current political structure to change the way they think. To change the way they behave. To change the way they interact. To change their experience (and therefore step aside to allow people who are better suited to Conscious Politics to take over). To basically change everything that they are and currently do.
Existing Politicians and the Political Parties they are a part of will not step aside or change. They are unconscious of the impact of their presence and what the real cause of all the problems are that they are failing to address.