Quite simply, yes
This is a perfectly normal, natural thing to say, at least where I am from, which is New York City. The City is often “overloaded by cars,” and that’s not at all an unusal observation to make, or way to phrase it.
It’s not the same as being overrun by cars—the cars aren’t every where per se (New York City has the lowest per-household rates of car ownership in the USA by a huge margin), or “taking over” (again, most people don’t use them) but they are in excess of the city’s capacity to handle cars (even a small fraction of NYC’s population is still a huge number of people), resulting in heavy traffic and impossible parking (my wife spent two hours looking for a spot just yesterday! my turn for that tomorrow).
Instead, the emphasis here is on capacity—the City only has so many parking spots, only so much room for traffic to move smoothly, and so on—and that is being overwhelmed. Stuff that is held against your capacity is the load on that capacity—in any kind of metric, not just weight—and in this case, we have overload. So yes, I think this is a rather ideal verb to use.
And by is a perfectly reasonable preposition to use—with would be equally fine—since the things taking up capacity are the cars. The preposition by could also refer to the people who did the loading—in this case, I guess, the drivers?—but context here would be quite clear that the cars didn’t do the loading, they are the things that have been loaded. By could work either way.
So yes, “the city can be overloaded by cars,” that’s perfectly fine.