Yes, there will be a problem, it's called misrepresentation to omit the child from the application. He should include his son as a non-accompanying dependent, and make every attempt to show he tried to get a medical done for the child. If you exclude the child from the application and it shows up during his background check that he fathered a child, he could be banned for misrepresentation and you find yourself having to wait 2 years before you can apply to sponsor him again.
At least make some effort to find the mother. If you don't, you can clearly demonstrate to CIC that you tried. Consider too the long-term consequences. What if some day the child tries to get back in touch with his father, and finds he is excluded from ever being considered from the family class because it was too inconvenient for him to try to locate him now?