Since most cameras focus with the lens wide open, a wider aperture allows the possibility of better AF performance. This is because the baseline between the light entering on opposite sides of the lens is wider.
But this potential can only be realized if the camera's AF system is designed to take advantage of it. Some cameras' AF systems are and some are not. So ultimately, it depends on the particular camera.
The following is primarily with regard to SLRs that have a dedicated PDAF sensor that is used when the camera's reflex mirror is down. Mirrorless cameras' main imaging sensor based AF systems are also affected by a lens' maximum aperture, but in different ways.
In general, the lines of demarcation are between f/5.6 and f/8 with respect to the minimum wide open aperture a lens can have and still allow a specific camera body to AF at all, and between f/4 and f/2.8 on the other end with regard to the minimum wide open aperture a lens needs to take advantage of the more sensitive sensors in a camera's AF system.
Many cameras require an f/5.6 or faster lens in order to AF at all, but there are some that can AF with an f/8 lens or combination of lens + teleconverter/extender. Most cameras that have some AF focus points that are more sensitive require f/2.8 or wider lenses in order for those points to function, but there are a few cameras that have PDAF sensors with a combination of f/2.8, f/4, and f/5.6 or f/8 lines on the AF sensor.
For a more complete discussion of how PDAF sensors work with lenses of various maximum apertures, including illustrations, please see this answer to: Does autofocus work better with f/2.8 lenses vs f/4 or slower?