Depends on the no clean paste being used. Most likely it will turn the no clean solder paste or flux residue to a white or hazed color. Mainly visual. I'd be more concerned with the active water soluble flux being manually cleaned off in a sink to be honest.

Residues of no clean fluxes are meant to be left on the board. The reason is that paste residues have a resin in them that is not water soluble thus making it very difficult/impossible to clean with water alone. One of the attributes of resin in the flux is that they also encapsulate the activators making the residue non-corrosive and non-conductive. By using water to clean you might be making your non-corrosive/non-conductive no clean flux corrosive and conductive.

You have to ask the question of How Clean is Clean?

It is probably not a good practice, but will the world stop because of it NO. Tap water has all kinds of mineral in it and in some cases it has added halogen, yup, fluorides. If it is dried off with high pressure air, the residues left behind would be miniscule.

If the customer has a problem then use Deinonized water and the minerals and other additives would not be an issue.

This approach is not a good practice for one obvious reason and one less obvious reason.

The more clear-cut bad practice is the use of tap water to clean a circuit board. Tap water contains many ionic contaminants that would be left on the board after cleaning, which can lead to long-term reliability issues. De-ionized (DI) water is really the only option for the cleaning of any type of electronic assembly and should be used in this situation.

The less obvious potential issue is the unknown interaction between the no-clean residue and the water. Most no-clean residues are not removed in water, but many of them can chemically react with water in such a manner that can impact board cosmetics and reliability. In some circumstances, the partial wash of no-clean residues can leave residues that are not completely chemically reliable. It is therefore advised to verify that the no-clean residues are reliable when subjected to a partial wash in any kind of water - even DI water.

The best way around all of this may be to introduce no-clean materials at the through-hole soldering operation, thereby forsaking the improved activity of the liquid flux but gaining long-term reliability. Although no-clean liquid fluxes are not as robust as water-soluble varieties, they can be sufficiently optimized to produce excellent results and eliminate cleaning completely.