The biggest argument against republic being a possible implementation of democracy was made centuries ago by Pericles. He stated that any system favouring money will end in ploutocracy (having only the richer's interests being represented). Republic filter's out a lot of people from the game of being eligible. It selects on a random criteria that will always end to be money at the end.
Republic whatever its implementation can be always will result in a feedback loop based on resources: money, media time, «fame», knwoledge, wisdom... As a result whatever the rule you make it will always end up favouring in the representation the guys with money. (you need exposure of your argument to win, that always ends up in making a 1:1:1 relation of exposure=money=probability of winning)
Democracy's goal however is to have all the population being represented. So as you can see these 2 systems are de facto mutually exclusive.
The big question is «are the human naturally bad?» If answer is yes: you choose republic to ensure only a subset of «capable citizens» are elected, but in the process you will mathematically converge towards a ploutocracy that will favor the more powerful/rich. Else, if all citizen are considered equally «capable» you can pick up any random citizen for forming a government. Hence living in a republic is NOT possibly living in a democracy.
Republic is just an aristocracy: it ensures the representant of the people are selected in a small subset of the population that tends to have more patrimonial. subset of the population that will tend to pass law to ensure the conservatism in the society so that their money is secured.