My Answer: That’s a very generalized question. In some cases, yes. In others, no. It depends on what is required of the vehicle. In most standard, consumer-grade applications, an EV is not likely to need a traditional, multi-geared transmission. Most of the time, the gearing in the differential(s) on the vehicle will do whatever reduction might be required or whatever torque vectoring is needed.
In some applications, such as heavy-duty use and when torque improvement is a big deal, it’s possible to use gearing to reduce the required size of the motor being used. For example, a heavy truck capable of moving 80,000 pounds of gross vehicle weight could use smaller motors (and thus less power) were the torque output to be raised via gearing. This is largely how big diesel engines outputting around 1,000 or so pound-feet of torque can move such heavy loads: gearing. Similarly, torque improvements via gearing (gearbox or differential) can do the same for electric motors.
Toyota’s Beta Fuel Cell truck, for example, outputs about 1,350 pound-feet of torque from its massive electric motor and uses a rear axle differential to raise that by an unspecified amount at the wheels. Off-road and even heavier machinery would also benefit from gearing that boosts power output.