If the spindle to tonearm pivot point distance is off by 2 – 3mm, will this affect the sound quality.
Yes.
And if the tonearm alignment is adjusted with a 2 point alignment tool to fit this distance error, would this alignment be okay?
There's no such thing as a 2-point TONEARM alignment. A tonearm is aligned at one point only, the design distance from the center of platter rotation to the center of tonearm rotation (aka, the spindle-to-pivot distance). I presume you were asking about a 2-point CARTRIDGE alignment. When discussing technical tools and measures please try to be precise in the use of terms, as to do otherwise causes confusion.
Some (not all) 2-point protractors might allow an accurate cartridge alignment to the chosen geometry (e. g., Baerwald, Loefgren, etc.) despite an inaccurate tonearm mounting distance. This would, however, result in a cartridge mounted non-square to the headshell. The resulting vectors would alter the amount of skating force from the tonearm's design and might alter energy transmissions between cartridge and headshell. This will result in changed sound, though in non-predictable ways.
IME, better sound results when the tonearm is mounted at the proper design distance and the cartridge is aligned using the alignment scheme envisioned by the tonearm designer. Can it be done otherwise? Of course.