While I do not practice law in DE, there are several points that I can post that may be of value in determining the answer to your question. If this were happening in NJ, the problem of getting a license stayed from being suspended would involve the NJ Motor Vehicle Commission (MVC). The point reduction would post after the MVC was officially notified by the agency through which you took the point reduction course. If the official notification was by computer, the notice would of course arrive faster. If the notice is by snail mail, the notice can take more then a couple of days. I suggest that you find out the answer to this question which will likely tell you the actual answer to your question.
The second point involves the qualifications for holding a CDL in DE. Will the DE Motor Vehicle Agency allow the CDL to stay valid if he gets the 3-point reduction? Did you get this in writing? I suggest you follow-up on this issue as well. Good luck.
This answer does not create an attorney-client relationship or constitute either legal advice or attorney advertising. Given the nature of this site, it is offered solely for information purposes, for you to use as a starting point when speaking with a lawyer in your State. To receive legal advice, it is critical that you consult with a lawyer admitted to practice law in your State as soon as possible, certainly before you take action on the matter you asked about. Do not presume that the law of the State of NJ will apply to the circumstances you are faced with.