Yes. Damage tolerance is built into Data Matrix itself.
The symbol contains both payload data and ECC200 error-correction information. This means part of the printed image can be lost while the data is still recoverable.
That is why a scratched, folded or partially torn Chestny ZNAK symbol is not automatically “dead”. Very often the real limitation is the scanner, not the code.
Specialised software can spend more effort on geometry, grid fitting, unknown modules and product-specific structure than a universal checkout scanner can.
If GTIN, product group or serial context is available, the search space becomes much smaller and the chances of success increase further.
For that reason, a damaged code is usually worth testing before you write off the item or start re-marking.