No. The vehicle speed is determined by a single sensor, the Vehicle Speed Sensor. It measures the rpm of the driveshaft (or one of them), the shaft that is the output from the transmission. You don't need the gear ratio.

But yes, it does assume that the tires are a certain size, so if you put the wrong size tires on, it will be wrong. Also, it's not super-accurate: tires sizes differ slightly by brand/model, plus they change their outer diameter as they wear down. That error accumulates.