AFAIK, if done properly, the adjustment of the vertical should not have any influence on the horizontal adjustment.
It is not uncommon that the horizontal adjustment is slightly off in some M cameras with certain lenses. Even if I had this with all my lenses, I would not let it bother me UNLESS I notice that the RF is off at medium or short distance, which is not necessarily the case.
As long as your rangefinder works properly wide open at short and medium distances (easy to find out when you put your camera on a tripod and do a series of test pictures), be happy and do not touch the mechanism. The minimal horizontal offset at infinity might be annoying, but is mostly irrelevant for pratical photography unless you use long lenses at wide apertures and long distances a lot. If you shoot at infinity, simply set the lens at infinity. When you start to tamper around with the horizontal adjustment, you stand to loose much more than you could possibly gain, because there is a risk that, when not done properly, adjusting the infinity setting to perfect matching will throw the rest of the system out of whack. If you notice missed focus shots on a regular basis and have the feeling that it is not user error, test your rangefinder carefully (tripod!) and if you find any irregularities please have it ajdustd by a competent repair person.
There are factory manuals for the M2 available on the internet that explain the adjustment procedure of the Leica rangefinder mechanism in all its glory. I recommend you have a lookt at it just to understand that contrary to Internet lore this is a rather complex and demanding procedure (if done properly). You will ask yourself why Leica wrote pages of text describing adjustment and testing, when all the Internet experts claim that anyone with a screwdriver can do the job during a coffee break! You will also learn that it is possible to mess up the mechanism in such a way that the camera has to be disassembled to have the RF re-adjusted from scratch. And, one might add --- this is not written in the repair manual, but taken from a recent post by some very unhappy fellow in a different forum --- it is indeed possible to screw up the job so thoroughly that even Leica factory service has to determine the RF unrepairable and replace the whole unit ...