It does not matter what sort of a constitution or document you have, since in any state, not just communist, you will always have a political establishment, and that political establishment will always find a way to distort the mechanics of government in its favour to redirect wealth and power to itself.

All governments are dominated by political establishments, and there are no real differences between political establishments and private corporations in terms of seeking profits, regardless of the costs to the majority of people. Therefore, in any country, any lessening of democracy, (most have very little to start with) or the giving of more responsibility to government, is the exact equivalent of selling your country to a private company; as though you were to sell the US to Monsanto or Google. This is the great logical failing at the heart of communism, taking the worst possible nightmare they could think of and proposing it as a solution, which most pro-communists and extreme socialists fail to see or address.