Might depend on which radio you have/are using and/or configuration.
For my home area/county, the system has 4 sites. I typically program all of them so when I travel around the area, I can use the best site.
In some cases, you could potentially hear additional/different activity on other sites.
In other cases, there are sites that carry little or no voice traffic.
For my Whistlers (which tend to select the best site of what you have programmed for you), I tend to import a system, lockout all but one site of that system, and assign the talkgroups to a scanlist. Then, I'll duplicate the system - one time for each site - and assign the talkgroups to a different scanlist. This way, I can decide which site (or sites) I want to monitor at any given time.
For some Whistlers (and GRE models), you can program multiple sites and tell the radio to check each site as if they are different systems.
For newer Unidens like the 436 and 536, the scanner will try to scan all of the sites you have programmed unless you take steps to control that (i.e. location control with zip code or GPS, create separate favorites lists, etc.).