No tests necessary, the laws of physics say the faster you accelerate the more power you need to do so.
You're absolutely right, but the part you're missing is that if you accelerate from 0-60 in 3.5 sec vs accelerating from 0-60 in 7 sec., you use twice the power in the first case, but accelerate for 1/2 the time.
So the *energy* you expend is the same. Wh is a unit of energy, not power, and energy is what matters when we talk about efficiency over distance.
(Note that if you accelerate more quickly, your average speed will be higher for the entire trip, which will hit efficiency because of energy losses due to aerodynamic drag, which scale with the square of the speed.)
Daniel is not exactly right about the acceleration, either - Electric motors *are* less efficient at high torques, particularly at low speeds. (Interestingly enough they are also less efficient at very low torques).
See, for example, this presentation which includes efficiency contours for a Nissan Leaf motor + inverter (
https://www.energy.gov/sites/prod/files/2014/03/f13/ape006_burress_2013_o.pdf)
Note that this efficiency loss is not huge (e.g., at 2000rpm, the Leaf motor/inverter combination shows a 90% efficiency at 100Nm vs an 86% efficiency at 250 Nm), so the biggest effects are likely due to the speed, not the acceleration.