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Published accuracy  of Atomstack P9= .01mm =10 thousandths of a mm or  .0003937 inches = ~4 ten thousandths of an inch or less than  1/2 a thousandths of an inch.                                                             
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Focusable DIY 5mW 650nm Red Cross Line Laser Module Adjustable Focus laser Head | eBay
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Ideally, laser cutting can focus on about 25 microns, which is about ¼ of the width of
a strand of human hair. Additionally, the cut width can be extremely small, at less than 0.001 inches. On the other hand, the dimensional accuracy is typically quite precise, at about 
± 0.0005 inches.

The short answer is very accurate. Today, cut width can be extremely small with laser cutting (less than 0.0001 inch) whilst dimensional accuracy is almost as precise (at approximately ± 0.0005 inch).
If you work in the metric system and your coordinates are all in mm, the finest resolution you can get is .001 mm or .00004 inches.
If you work in inches, the finest resolution you can get is .001 inch.
1.0000″=One Inch
.1000″=One Hundred Thousandths
.010″= Ten Thousandths
.001″= One Thousandth
.0001″=One Tenth (One Ten thousandth)
.00001″=Ten Millionths
.000001″=One Millionth
.000001″ = 1 Microinch
.0002″ = 200 Millionths Micro inches and Millionths are interchangeable
Inches X 25.4 = millimeters
Millimeters divided by 25.4 = inches
Microinches X .0254 = micrometers
Micrometers divided by .0254 = microinches
39.37 microinches =.00003937 inches = 1 micrometer (micron)
.001 millimeters =1 micrometer
.0254 micrometers =.0000254 millimeters
1 micron= 40 millionths of an inch


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20pcs 1235 Focusable 650nm 5mW Red Laser Cross hair Module Diode with Driver | eBay
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Video
Mach 3 Script
STL  for laser mount.
Printed version of mount
Double Sided Sticky foam.  
Laser Module
Alignment Code Generation:
Use a scrap  piece of material with a mark where you want the laser to start cutting.
Align cross hair laser to Mark.
Run your engraving or cutting  program on the laser.
Targeting template to print and paste to cardboard. 1mm g or 1/10th inch graticule.
Measure distance between cross hair align point and where the  beam started engraving or cutting x distance= _____  y distance= ____.

Be careful when testing...
A simple coding error can cause
the LASER to fire. It is highly recommended to test any code  in a g-code viewer  first.

If you can mount the laser crosshair directly on axis to the x or y axis of the laser beam you can save steps in setting the offset.

Create a g-code  "alignment program"  to move the distance to x and y to the Cross Hair marked point by the laser beam. 
Reference    Sainsmart Reference
For MM use G21 for inches G20.
You may have to strip the annotation for it to run as that different versions of GRBL
use different disable characters like / or ; or (  ).


G21 x0 y0 (set zero  G20 for inches G21 for mm)
G00 X-22  (g20 for inches g21 for mm non cutting -22mm)
G00 Y-22  (g20 for inches g21 for mm non cutting -22mm)
M02 (end of program)

Example of code without annotation:
This should always run for mm
G21 x-0 y-0
G00 X-22 
G00 Y-22
G92 X-22 Y-22
M02

or as below for inches

G20 x-0 y-0
G00 X-3
G00 Y-3G
92 X-3 Y-3
M02

To use:
Align cross hair to start point.
Run the Alignment program.
Start your cut or engraving program.

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