Since the camera measures where to drive the lens to get it into focus, it's hardly the drive motor type in the lens which determines how successful the camera is in calculating the proper focus setting.
There's also the confusion about f/2.8 high-precision and f/5.6 standard precison focusing. But that has nothing to do with how much light comes through the lens. It's instead a question about how far apart the rays are at one and the other side of the lens. High precision focusing requires a longer baseline for the AF sensor pair, and thus a wider opening in the lens for these rays to hit the AF sensor.
Furthermore, if you read the camera's specification, you'll notice that Canon specifies which EV range the AF system works with. But the EV value is the same, regardless of which lens is mounted on the camera! Thus the camera's AF sensor is capable of working with the rays it gets through the lens, down to a certain ambient light level, and that's not dependent on the total light coming into the lens. The AF system's secondary image forming optics pick out two rays from the lens, one from each side, and it will do so regardless of the max aperture of the lens (with the exception of the high-precision focus mentioned above - but there too it's a question about where the rays come in, not how much light enters the whole lens).
On the other hand, lower cost lenses typically have inferior image quality compared to the more expensive ones. Chromatic abberation and various other imperfections in the lens will not only distort the final image. They will also distort the image the AF sensor has to evaluate.
If you want to see a test which proves that the reasoning above in this thread is at fault, you are welcome over to me. It's pretty dark in Sweden this time of the year, so well have no problem finding low light situations. Then I can show you that a 400D or a 7D equipped with an f/1.8 lens will sometimes fail focusing on something a 1DX can handle with f/4 or f/5.6.
Finally, there are indeed lenses which have problems setting focus at the right distance. Sometimes, like with the EF 50 mm f/1.4 USM, it's due to a rather coarse stepping of the focusing motor. Sometimes it's due to a fault in the calibration of the lens, not the lens technology itself.
Thus the answer to the original question would be yes, it can make a difference, but not for the perceived reason.