You have that somewhat backwards with regards to the senate. Anyone elected to a magistracy was elevated into the senate for life. Now regarding voting - yes all male Roman citizens (ok, there were a class of citizens without the vote but they tended to be at colonies too far to vote in Rome) had the right to vote. But the 'value' of their vote would depend greatly on which assembly they were voting in. Citizens voted in three different assemblies based on 2 different social divisions: centuriate (based on wealth) and tribal (more regional).

The big one was the centuriate assembly which was comprised of 193 (going on memory) centuries. This assembly elected senior magistrates (Consuls, Praetors) and determined war/peace. These were arranged by wealth in descending order, so the richest were in the 1st century while the poorest would be grouped into the last 5 centuries. Each century had one vote based on a simple majority within the century. As you can see this means a wealthy Roman's vote was much more significant than a poor man's. Even worse, voting would proceed until a majority was reached - so the lower centuries would rarely ever even have the opportunity to vote.

Then there are the tribal and plebeian assemblies. These arranged the citizen body by their tribes of which 31 were rural and 4 were comprised of urban citizens. As before, each tribe had a single vote based on a simple majority. However tribes voted in random order making it much more democratic. These assemblies voted in lower magistrates (aediles, quaestors) and the Tribune of the Plebs. In the Late Republic, the Tribunes of the Plebs began to bring laws the senate wouldn't approve before the Plebeian assembly to pass (where it would be binding on all Roman's).

So the people were represented. Kinda. And depending on which assembly. Note that this was further determined by your distance from Rome - if you lived a couple of days travel away, the probably wouldn't be making the trip to vote regularly.