There are two answers to that question, on dSLRs the focal plane and focus sensor can be a bit off (misaligned), hence why you may need micro-adjustments - usually however it will not be misaligned by the z axis so it shouldn’t be based on AF points, but in theory it could be.

In mirrorless cameras, the focus is done on the images sensor so you will not have any misalignments.

However, not all AF points are created equal and off centre focus points are usually of lower quality (meaning often non cross type and almost always non f/2.8). High end dSLRs do have many cross-type off centre, lower end have fewer - for example Canon 7D mk. II has 65 autofocus points, but they are all of the cross-type, meanwhile the Canon 1200D offers 9 AF points, with just the centre point being cross-type). The centre focus is always a cross type and most often also f/2.8 optimised.

So off centre AF point will typically be less accurate than the centre AF point. And with phase AF, the closer to the edge of the sensor/frame it is, the more difficult it is to get proper focus – this is why you don’t have the full coverage of AF points, they are usually clustered around the centre of the frame.

However, by using hybrid focus* (both phase and contrast detection) Sony have in their mirrorless E-mount made it possible to have full coverage by making the edge AF points contrast detection only (like A6300 and A7R II) and the centre a combination.

Mentioning field curvature has been suggested, however field curvature is very lens dependant, I have two macro lenses, both tack sharp corner to corner - and a few primes with at least fair corner to corner sharpness. So it's certainly not all lenses that suffer visibly from this.

However, many lenses (especially zooms) have visible corner softness at certain apertures, these lenses will naturally affect off centre AF when the sharpness and contrast is failing to provide the autofocus with the informations needed.

Both contrast and phase AF will be affected by field curvature when the lenses performance drops. Meaning AF performance is not lens independent.

• Not to be confused with Sony's A-mount hybrid AF system in A99M2, this is phase AF only, however combined on sensor phase AF and a dedicated tradition phase detection AF sensor. Sony uses the same terms incl. 4D auto focus, but the two systems works differently.