Short answer is No
Illustrator's dialog boxes are programmed to only support a certain amount of decimal places. So the rounding is purely a cosmetic thing. Internally however Illustrator stores values and honors exact precision.
Illustrator uses 3 decimal places and 4 in newer versions, however there is no way currently to extract more than the 3-4 decimal places.
It sounds like there is a mismatch with how the cutting table's software handles decimals and Illustrator does.
My advice is to standardise decimals with a script like this:
// script.name = roundSelectedFrames.jsx;
// script description = rounds selected textFrames to 3 decimals;
// script.required = select at least one text frame before running;
// script.parent = CarlosCanto // 6/14/11;
// script.elegant = false;
var idoc = app.activeDocument;
sel = idoc.selection;
for (i=0 ; i<sel.length ; i++ )
var iframe = sel[i];
var content = iframe.contents;
var search4decimals = /\d.\d\d\d\d/;
var decimals4 = content.match(search4decimals);
var decimals3 = Number(decimals4).toFixed(3);
var replace = content.replace(decimals4,decimals3);
iframe.contents = replace;
alert("select at least one text frame before running");
Then you won't have any more minor mismatches.
Coming from having worked start to finish from art to production to shipping you need to be diligent and standardize the art before you have to cut it. If you aren't doing the art, reach out to your clients and give them a list of "best practices" to follow to ensure their products come out perfect every time.