Generator mounted off center in cartridge body.

I would like to hear from others in regards to their experience with this. This mostly would pertain to cartridges that have a square body around the generator. For example Shelter and Benz Micro. Do you think that it makes any difference other than alignment taking more time.
As long as the cartridge is not defective, and only the body seems to be a bit wider on one side than the other, it should not pose a problem.

Assuming that the sides are still parallel, you can use them for alignment, and assuming the front is straight, you can use that too.

The stylus tip has to sit on the dot, and the body must align with the lines. And it must be straight at both null-points.

I'd be a bit concerned about a defective cartridge, if this is a major amount off, because of the need to have the coils centered in the magnet fields. But if it is not defective in the motor part, the outer body is just providing an alignment guideline, and possibly a shield in some cases.
I'll take a slightly stronger position than Twl. If a cartridge comes to you new in that condition, strongly consider requesting a replacement.

My Shelter 901 (bought used) has two visible defects:

1. cantilever is not square to body when viewed from above

This was easily dealt with by aligning the cantilever, not the cartridge body. You should do this anyway, few cartridges have perfect zenith IME. A good mirrored protractor makes cantilever alignment easier and more accurate.

2. generator is both rotated and off-center relative to body and cantilever, when viewed from the front

This presents an insoluble performance/safety dilemma.

OT1H, as Twl said, the coils are not centered in the magnetic fields of the generator. This increases crosstalk between channels, which muddies voicing, imaging and soundstaging. My 901 measures 8-9 db of crosstalk, which is horrible for a $1500 cartridge. Cello's 901, which appears square, measured just 1.5 db when mounted on my rig. My three ZYX cartridges all measure around 0.2 db, which is almost surreal-ly good. (Is that a word?)

OTOH, the way you reduce crosstalk is by adjusting azimuth. But even if your arm allows this, you don't want to set your stylus significantly off straight vertical. You can imagine how bad that could be for the long term health of your groove walls.

IOW there was no satisfactory fix for my second problem except a replacement. Until then I set azimuth visibly for a vertical stylus. Anything else would have been unsafe.