Let me say again that the relationship is asymmetrical: there's no democracy without a market economy, but you can have a market economy without democracy.
Even in a society as tightly controlled as Singapore's, the market creates certain forces which perhaps in the long run may lead to democracy
So I think one can say on empirical grounds - not because of some philosophical principle - that you can't have democracy unless you have a market economy.
If you say simply that pressures toward democracy are created by the market, I would say yes
