We know that Sith orchestrated Clone Wars, and in secret controlled both sides. Their ultimate goal was gaining power over galaxy and destruction of Jedi Order. Yet, books like Darth Bane and Darth Plagueis (both part of Legends now) tell us the story where Sith didn't want Republic to die, they just wanted to keep it weak and corrupt until right time comes for takeover. To that end, they sabotaged many separatist movements, forcing them to reveal themselves prematurely.
Question is, what would happen if Sith chose not to act politically (not to pursue position of Senator and latter Chancellor), or simply didn't exist ? I imagine Republic would still be weak, with no large central military. Entities like Trade Federation, Banking Clan, Techno Union etc ... would exist and wield tremendous power, first financially, then politically and latter militarily. Corruption would be substantial, also desire on some systems to brake off. It is entirely possible that in certain moment large corporate entities would start to use their military strength against smaller systems like Naboo, even without goading of Sith. Jedi would be forced to act, but this time without help of Clone Army. Could Republic survive this without spiting up ?