Quaestors were automatically enrolled in the Senate after the time of Sulla's reforms. That means as soon as they took office, they could participate in meetings. Having said that, most of them were not in the city while in office, but instead out in the provinces or with armies, doing their jobs. Some of them were assigned to the City and would be expected to be present and participatory at all Senate meetings. Once they were done with their year of office, they continued to be members of the Senate unless one of the censors removed them. Some would go on to further offices (aedile, praetor, consul), but of course there were 20 quaestors per year and only 2 consuls—many quaestors therefore never made it all the way to the top.