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.
I wonder what you mean by "accumulates". If I change the tires, the slight difference due to the previous brand and the slight difference due to the new brand do not compound. I only get the last one. And if the older ones were worn, the new ones will have less error, as they are less worn.
If the errors really accumulated, once in a while we would need to recalibrate the speed sensor, else we would be doing 90 and showing 10. In fact the error is limited to some reasonable amount.
Accumulate in this context means that there are several small errors, and it's a function of summing or multiplying those accumulated errors. It does not mean that they accrue over time.
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.