Yes. the pre-Marian reform Roman army was just another civic militia that was common to Graeco-Roman city-states. In most of these (Athens and their democracy represented the exception) political representation was tied to both military service and wealth.

The Romans, divided up their male citizen population into 193 centuries based on their wealth. The senatorial class made up the topmost, then the equestrians, then the independent small holders. The landless poor were grouped into the last 4 centuries. Each class was supposed to possess a certain level of equipment for when they were called up. So the equestrian class supplied their own horse (and later this distinction changed and they start to appear as junior officers within the legion and the Romans relied on allied cavalry), while the infantry came from independent land-holders. The urban poor, aside from some serving as skirmishers, would not often be called upon for military service - and also had effectively no political power. This system served Rome pretty well up until the Late Republic.

The problem is this system worked great for a small city-state squabbling with its neighbours. Each summer you might get called to serve, march out to fight in your immediate vicinity and come back with a little bit of booty. The problem is Rome was really successful and the soldiers were fighting farther and farther away, furthermore you were called up for a campaign and until it wrapped up you didn't get to go home.

So by the Late Republic, Rome controlled an empire that ran from Greece to Spain and down to Africa. They had two long-running wars (Spain and Africa) that lasted years. This meant soldiers might get called up and not see home for multiple years - and as all legal authority lay in the father, many small farms began to fail. When a smallholder was forced to sell, he no longer met the property qualifications to serve and joined the landless urban poor in Rome. This meant that while Rome was growing in territory, her manpower pool for the army was steadily shrinking and Rome was more and more dependent on allied infantry.

It was in this climate that Marius waived the property requirements and just took volunteers (whether he supplied them equipment or the state did I'm not sure, but Rome was wealthy enough to do so at this juncture). The urban poor saw this as a chance to make some money (in the form of booty) as well as be rewarded after the campaign with land and become respectable independent farmers again.